Help what’s the answer

3KOH(aq) +H₃PO₄(aq) → K₃PO₄(aq) +3H₂O (l)  ; A.) KOH should have a coefficient of 1.

To balance the equation, KOH should have a coefficient of 1.

Here, there is 1 potassium (K) atom, 1 phosphorus (P) atom, and 4 oxygen (O) atoms on each side of the equation.

To balance the equation, start by placing coefficient of 3 in front of KOH and coefficient of 1 in front of H₃PO₄ ;

This balances number of potassium and phosphorus atoms, but there are now 9 oxygen atoms on left side and 6 on right side. To balance the oxygen atoms, add coefficient of 3 in front of H2O.

Now the equation is balanced, and coefficients are:

3KOH(aq)+ 1H3PO4 (aq) → 1K3PO4 (aq) +3H2O (l)

Therefore, only A. KOH should have a coefficient of 1.

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The number of moles of undissolved NaCl in the solution is 0.22 mol.

The number of moles of undissolved salt is calculated as;

mass of NaCl dissolved = volume of solution x solubility

volume = 100 cm³ = 100/1000 dm³ = 0.1 dm³

mass of NaCl dissolved = 0.1 dm³ x 9 mol/dm³

mass of NaCl dissolved = 0.9 mol

So, 0.9 moles of NaCl dissolved in the solution.

moles of undissolved NaCl = total moles of NaCl - moles of dissolved NaCl

molar mass of NaCl = 23 g/mol + 35.5 g/mol  = 58.5 g/mol

total moles of NaCl = 65.52 g / 58.5 g/mol = 1.12 mol

moles of undissolved NaCl = 1.12 mol - 0.9 mol

moles of undissolved NaCl = 0.22 mol

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The equilibrium concentrations for [OH-], hydroxylamine [HONH2], and the hydroxylammonium ion [CH3NH3+] in a 0. 025 M solution of hydroxylamine is 8.34 x 10^-5 M, 0.0249 M,  and 8.34 x 10^-5 M.

To calculate the equilibrium concentrations for [OH-], hydroxylamine [HONH2], and the hydroxylammonium ion [CH3NH3+] in a 0.025 M solution of hydroxylamine, we first need to write out the balanced chemical equation for the reaction:

HONH2 + H2O ⇌ HONH3+ + OH-

Next, we can set up an ICE table to help us solve for the equilibrium concentrations:

Initial:    HONH2 = 0.025 M    H2O = 0 M    HONH3+ = 0 M    OH- = 0 M
Change:   -x                +x           +x           +x
Equilibrium:  0.025 - x      x            x            x

We can then use the Kb expression for hydroxylamine to solve for x, which represents the concentration of OH-:

Kb = [HONH3+][OH-] / [HONH2]

1.1 x 10^-8 = x^2 / (0.025 - x)

Solving for x using the quadratic formula, we get:

x = 8.34 x 10^-5 M

Therefore, the equilibrium concentrations are:

[OH-] = 8.34 x 10^-5 M
[HONH2] = 0.025 - x = 0.025 - 8.34 x 10^-5 = 0.0249 M
[HONH3+] = x = 8.34 x 10^-5 M
[CH3NH3+] = 0 M (since it is not involved in the reaction)

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The volume/concentration of the above questions are as follows:

The amount of volume or concentration of a substance can be calculated using the following expression;

CaVa = CbVb

Where;

1. 10 × 250 = 0.5 × Vb

2500 = 0.5Vb

Vb = 5000mL

2. 0.400 × 15 = 2 × Cb

6 = 2Cb

Cb = 3M

3. 50 × 20 = 1000 × Cb

1000 = 1000Cb

Cb = 1M

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D. A mountain range with folded layers of rock.

Intense compression can cause the rock layers to fold, creating a mountain range. This type of feature forms suddenly in the geological timescale, as a result of tectonic activity, and is known as a fold mountain.

The intense pressure causes the rock layers to buckle and deform, resulting in folds, faults, and other features. The Appalachian Mountains and the Rocky Mountains are examples of fold mountains in the United States.

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D. Al of the following is a reactant in the chemical equation

In a chemical equation, the substance or substances to the left of the arrow are referred to as reactants. A material that is present when a chemical reaction first begins is known as a reactant. Products refer to the material or substances to the right of the arrow. A material that is present following a chemical reaction is known as a product.

Methane (CH4) and oxygen (O2) are the reactants and carbon dioxide (CO2) and water are the products in this chemical process. (H2O). This illustration demonstrates that chemical bonds may form and break during a chemical process. The forces that keep the atoms of a molecule together are known as chemical bonds.

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The number of servings of cereal needed to consume 0.0350 moles of sugar is approximately 0.834 servings.

1. Calculate the molar mass of sucrose (C₁₂H₂₂O₁₁): (12x12) + (1x22) + (16x11) = 144 + 22 + 176 = 342 g/mol.

2. Convert grams of sugar per serving to moles: 11.0 g/serving * (1 mol/342 g) ≈ 0.0322 moles/serving.

3. Divide the desired moles of sugar by moles/serving: 0.0350 moles / 0.0322 moles/serving ≈ 0.834 servings.

So, to consume 0.0350 moles of sugar, you need to eat approximately 0.834 servings of this cereal.

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The volume of gas in the neon sign is 2.0 mL.

Neon signs are a popular form of advertising, characterized by bright and colorful lights that make them easily noticeable. These signs are made up of glass tubes that contain a small amount of neon gas at extremely low pressures, typically around 27.0 torr.

When an electrical current is applied to the gas, it emits a bright red-orange light, giving the sign its characteristic glow.

In order to determine the volume of gas in a neon sign, we need to use the ideal gas law equation, PV=nRT. We are given the pressure, temperature, and number of moles of gas in the sign, but we need to find the volume. Rearranging the equation to solve for V, we get V=nRT/P.

Plugging in the given values, we get:

V = (1.075 x 10^-4 moles)(0.0821 L•atm/mol•K)(315.75 K)/(27.0 torr x 1 atm/760 torr)
V = 0.002 L or 2.0 mL

Therefore, the volume of gas in the neon sign is 2.0 mL. It's important to note that the volume of gas in the sign can vary depending on the size and shape of the sign, as well as the pressure and temperature of the gas inside.

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The final pressure of the gas is approximately 545.4 mmHg when the temperature is raised from 15 °C to 35 °C.

Combined gas law states that "the ratio of the product of volume and pressure and the absolute temperature of a gas is equal to a constant.

It is expressed as;

P₁V₁/T₁ = P₂V₂/T₂

Given that:

Subtsitute our given values into the expression above.

P₁V₁/T₁ = P₂V₂/T₂

P₁V₁T₂ = P₂V₂T₁

P₂ = ( P₁V₁T₂ ) / ( V₂T₁ )

P₂ = ( 850 mmHg × 1.5L × 308.15K ) / ( 2.5L × 288.15K )

P₂ = 545.4 mmHg

Therefore, the final pressure is 545.4 mmHg.

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The correct answer is option e. 3.075 m/s. Speed is a scalar quantity, which means it has only magnitude and no direction.

What is Speed?

Speed is a measure of how quickly something moves from one place to another. It is the rate at which an object covers distance over time, and is usually expressed in units of meters per second (m/s) or kilometers per hour (km/h).

Since the temperature and pressure are the same for both oxygen and hydrogen gas, the only difference between the two is their molar mass. The molar mass of oxygen is 32 g/mol, and the molar mass of hydrogen is 2 g/mol. Therefore, we can calculate the RMS speed of hydrogen as:

u = √(3RT/M) = √(3RT/2)

The RMS speed of oxygen is given as 12.3 m/s. To find the RMS speed of hydrogen, we need to calculate the ratio of their speeds:

u(H2)/u(O2) = √(M(O2)/M(H2)) = √(32/2) = √16 = 4

Therefore, the RMS speed of hydrogen is:

u(H2) = u(O2)/4 = 12.3/4 = 3.075 m/s

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The actual yield was 1.329 g Ag.

The balanced equation for the reaction between Zinc and Silver Nitrate is:

Zn + 2AgNO₃ -> 2Ag + Zn(NO₃)₂.

Given: 29 g Zn, and 2 g AgNO₃. Molar masses: Zn = 65 g/mol, AgNO₃ = 169.87 g/mol.

Moles Zn = 29/65 = 0.446 mol

Moles AgNO₃ = 2/169.87 = 0.0118 mol

Since the stoichiometric ratio is 1:2 (Zn:AgNO₃), we need 0.223 mol AgNO₃ for a complete reaction.

We have only 0.0118 mol AgNO₃, making it the limiting reagent.

Theoretical yield of Ag: 2 mol Ag produced from 1 mol AgNO₃.

0.0118 mol AgNO₃ * (2 mol Ag / 1 mol AgNO₃) * 108 g/mol (Ag's molar mass) = 2.54 g Ag

The actual yield was 1.329 g Ag.

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Among the halogens, [tex]I2[/tex] has the lowest boiling point.

The boiling point of a substance is influenced by the strength of its intermolecular forces, which are the forces that hold molecules together. The halogens belong to the same group in the periodic table and have similar electronic configurations.

The boiling point increases with increasing molecular weight because the intermolecular forces increase with the size of the molecules.

The strength of the intermolecular forces depends on the type of attractive forces between the molecules. Among the halogens, the strength of the intermolecular forces increases with increasing polarity of the molecule.

Fluorine is the most electronegative of the halogens and has the smallest atomic size. Due to its high electronegativity, it has the strongest dipole-dipole interaction between its molecules, leading to the highest boiling point among the halogens.

On the other hand, iodine has the weakest intermolecular forces, leading to the lowest boiling point among the halogens. Therefore, among the halogens, I2 has the lowest boiling point.

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The volume of the 3.5 m solution containing 9.82 g of Pb(NO3)4 is about 4.103 mL.

To calculate the volume of the solution, we need to use the formula for molality:

Molality (m) = moles of solute / kg of solvent

First, we need to find the moles of Pb(NO3)4 in 9.82 g. The molar mass of Pb(NO3)4 is approximately 683.56 g/mol.

Moles of Pb(NO3)4 = 9.82 g / 683.56 g/mol ≈ 0.01436 mol

Now, we can use the given molality (3.5 m) to find the mass of the solvent:

0.01436 mol = 3.5 m * kg of solvent
kg of solvent = 0.01436 mol / 3.5 m ≈ 0.004103 kg

Since the solvent is water, we can assume that 1 kg of water is equal to 1 L. Therefore, the volume of the solution is:

0.004103 kg * 1000 mL/kg ≈ 4.103 mL

So, the volume of the 3.5 m solution containing 9.82 g of Pb(NO3)4 is approximately 4.103 mL.

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4666.7 m of sulphur dioxide are formed when 12.5g of iron sulphide ore (pyrite) reacts with oxygen according to the equation at stp.

According to given data,   12.5 g of iron sulphide ore (Pyrite ) reacts with oxygen according to the equation at STP.

We have to find the volume of sulphur dioxide

Mass of iron sulphide = 12.5 g

molar mass of iron sulphide = 120 g/mol

so number of moles of iron sulphide = 12.5/120 = 0.104167 mol

chemical equation of reaction of iron sulphide with oxygen is given as

4FeS₂ + 11O₂ ⇒2Fe₂O₃ + 8SO₂

here  4 mol of FeS₂ gives 8 mole of sulphur dioxide.

⇒1 mol of FeS₂ = 8/4 mol = 2 mol of sulphur dioxide.

⇒0.104167 of FeS₂ = 2 × 0.104167 = 0.208334 mol of Sulphur dioxide.

at STP 1 mol = 22.4 L

so the mass of sulphur dioxide

= 0.208334 × 22.4 L

= 4.6666816 L

= 4666.6816 ml

≈ 4666.7 ml

Therefore the volume of sulphur dioxide is 4666.7 ml.

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The initial temperature of the air in degree Celsius was approximately 33.6°C.

When the hiker inhales air, the air undergoes a temperature change from the initial temperature to the body temperature, and a volume change due to the expansion of the lungs.

Using the ideal gas law, we can relate the initial and final volumes and temperatures of the air.

PV = nRT

Assuming the pressure is constant, we can rearrange the equation to:

(V₁/T₁) = (V₂/T₂)

where V1 is the initial volume of air, T₁ is the initial temperature, V₂ is the final volume of air, and T₂ is the final temperature (body temperature, 37°C).

We can substitute the given values and solve for T₁:

(V₁/T₁) = (V₂/T₂)

(T₁/V₁) = (T₂/V₂)

T₁= (T2 × V₁ / V₂

T₁ = (310.15 K × 0.598 L) / 0.612 L

T₁≈ 303.5 K

Converting to degrees Celsius, we get:

T₁ ≈ 30.5°C

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Red tape can be used to repair a broken taillight on a car. Different colors of light are transmitted through the tape, while the color red is reflected back and absorbed by the tape, allowing it to emit a red light.

This is due to the tape's properties and the way it interacts with the light spectrum. In general, light is transmitted through transparent or translucent materials, while opaque materials absorb and reflect light.

The color of an object is determined by the wavelengths of light that are absorbed and reflected by its surface. So, in the case of the red tape, it absorbs all colors of light except for red, which it reflects back, allowing the tape to emit a red light when placed over a broken taillight.

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The balanced equation for the reaction of iron (Fe) with chlorine gas (Cl₂) in an acidic solution, forming Fe³⁺ and Cl⁻, is:
6H⁺ + 2Fe + 3Cl₂ → 2Fe³⁺ + 6Cl⁻ + 6H₂O

In this reaction, iron (Fe) reacts with chlorine gas (Cl₂) in the presence of an acidic solution, which provides protons (H⁺) as reactants. The iron atoms are oxidized from their elemental state (0 oxidation state) to the +3 oxidation state, forming Fe³⁺ ions. Chlorine gas is reduced to chloride ions (Cl⁻).

To balance the equation, it is necessary to ensure that the number of atoms of each element is equal on both sides of the equation. In this case, we have two iron atoms and six hydrogen atoms on the left side, and two iron atoms, six hydrogen atoms, and six oxygen atoms on the right side.

By adding coefficients to the reactants and products, we can balance the equation:

2Fe + 3Cl₂ + 6H⁺ → 2Fe³⁺ + 6Cl⁻ + 2H₂O

Now, the equation is balanced with two iron atoms, three chlorine molecules, six hydrogen ions, two Fe³⁺ ions, six Cl⁻ ions, and two water molecules on each side of the equation.

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Atomic mass unit (amu) is used to describe atomic mass, with the symbols "u" or "Da" used to represent it. Carbon-12 was used as the reference element to define the atomic mass unit. A spectrometer can be used to determine the elements found in an unknown substance.

The type of bonds that form within a sample of sodium metal, chlorine gas, and sodium chloride crystals are metallic bonds, covalent bonds, and ionic bonds. The electron structure of each substance affects the properties of compounds that it forms in the following ways:

Sodium metal forms metallic bonds, which involve the delocalization of electrons among a lattice of positively charged metal ions. In sodium metal, each atom donates one electron to the shared electron "sea." This electron structure allows metals to conduct electricity and heat, and exhibit malleability and ductility.

Chlorine gas forms covalent bonds, which involve the sharing of electrons between two non-metal atoms. In this case, two chlorine atoms share a pair of electrons to achieve a stable electron configuration. The electron structure of covalent bonds results in compounds with relatively low melting and boiling points, and poor conductivity of electricity and heat.

Sodium chloride crystals form ionic bonds, which involve the transfer of electrons from one atom to another, resulting in the formation of oppositely charged ions. In sodium chloride, sodium loses an electron to chlorine, creating Na⁺ and Cl⁻ ions. The electron structure in ionic compounds leads to high melting and boiling points, and good conductivity when dissolved in water or molten.

These different types of bonds and electron structures significantly influence the properties of the compounds formed.

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The mass of solute in a 500mL solution of 0.200 M Sodium Phosphate is approximately 16.394 grams.

To find the mass of solute in a 500mL solution of 0.200 M Sodium Phosphate, we can follow these steps:

1. Identify the molar concentration (M) of the solution, which is given as 0.200 M.
2. Convert the volume of the solution from mL to L: 500mL = 0.500L.
3. Calculate the moles of solute (Sodium Phosphate) using the formula: moles = Molarity × Volume. So, moles = 0.200 M × 0.500 L = 0.100 moles.
4. Find the molar mass of Sodium Phosphate (Na3PO4). The molar mass of Na is 22.99 g/mol, P is 30.97 g/mol, and O is 16.00 g/mol. Therefore, the molar mass of Na3PO4 is (3 × 22.99) + 30.97 + (4 × 16.00) = 163.94 g/mol.
5. Finally, calculate the mass of solute using the formula: mass = moles × molar mass. So, mass = 0.100 moles × 163.94 g/mol = 16.394 g.

In summary, the mass of solute in a 500mL solution of 0.200 M Sodium Phosphate is approximately 16.394 grams.

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The standard molar entropy change for the combustion of methane gas is 9.9 J/(mol·K).

The balanced equation for the combustion of methane is:

[tex]CH4(g) + 2O2(g) → CO2(g) + 2H2O(l)[/tex]

The standard molar entropy change can be calculated using the formula:

ΔS° = ΣS°(products) - ΣS°(reactants)

The standard molar entropy values for the species involved in the reaction are:

ΔS°(CH4) = 186.3 J/(mol·K)

ΔS°(O2) = 205.0 J/(mol·K)

ΔS°(CO2) = 213.6 J/(mol·K)

ΔS°(H2O(l)) = 69.9 J/(mol·K)

Using these values, we can calculate the standard molar entropy change:

ΔS° = [ΔS°(CO2) + ΔS°(2H2O(l))] - [ΔS°(CH4) + ΔS°(2O2(g))]

ΔS° = [(213.6 J/(mol·K)) + (2 × 69.9 J/(mol·K))] - [(186.3 J/(mol·K)) + (2 × 205.0 J/(mol·K))]

ΔS° = 9.9 J/(mol·K)

Therefore, the standard molar entropy change for the combustion of methane gas is 9.9 J/(mol·K).

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Benign and malignant are terms used to describe different types of tumors.

A benign tumor is a mass of cells that grows slowly and does not invade nearby tissue or spread to other parts of the body. It is typically encapsulated, meaning it is surrounded by a membrane that separates it from surrounding tissues.

While it is still considered abnormal, it is usually not life-threatening and can often be removed with surgery. Benign tumors do not metastasize or spread to other parts of the body.

On the other hand, a malignant tumor is cancerous and has the ability to spread to other parts of the body through the bloodstream or lymphatic system. Malignant tumors grow rapidly and invade nearby tissue, which can cause damage to organs and structures in the body.

These tumors can also interfere with the normal functioning of organs, leading to serious health problems. Malignant tumors are usually treated with a combination of surgery, radiation, and chemotherapy.

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Both 1.0 mol of calcium (Ca) and 1.0 mol of magnesium (Mg) contain the same number of atoms (Avogadro's number, 6.022 x 10²³ atoms), but they differ in mass and chemical properties.

In order to compare 1.0 mol Ca and 1.0 mol Mg, we must first understand the concept of a mole. A mole is a unit of measurement that represents 6.022 x 10²³ particles (atoms, molecules, ions, etc.). This number, known as Avogadro's number, allows us to compare amounts of different substances.

Although 1.0 mol Ca and 1.0 mol Mg both contain the same number of atoms, their masses are different. The molar mass of Ca is 40.08 g/mol, while the molar mass of Mg is 24.31 g/mol.

Therefore, 1.0 mol Ca has a mass of 40.08 g, and 1.0 mol Mg has a mass of 24.31 g. Additionally, Ca and Mg are both alkaline earth metals but possess different chemical properties, such as reactivity and electron configurations.

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The synthesis reaction of chlorine gas (Cl2) and sodium metal (Na) results in the formation of table salt, which is sodium chloride (NaCl). To determine the amount of sodium chloride produced, we need to consider the stoichiometry of the reaction.

To determine how many grams of table salt are made from the synthesis reaction of chlorine gas and 400 grams of sodium metal, follow these steps:

1. Write the balanced chemical equation for the reaction:
2Na + Cl2 = 2NaCl

2. Calculate the molar mass of sodium (Na) and table salt (NaCl):
Na = 22.99 g/mol
NaCl = 22.99 g/mol (Na) + 35.45 g/mol (Cl) = 58.44 g/mol

3. Calculate the moles of sodium metal:
moles of Na = 400 g/22.99 g/mol = 17.40 moles

4. According to the balanced equation, 2 moles of Na produce 2 moles of NaCl. Therefore, the moles of NaCl produced are the same as the moles of Na used:
moles of NaCl = 17.40 moles

5. Calculate the mass of NaCl produced:
mass of NaCl = moles of NaCl  molar mass of NaCl = 17.40 moles  58.44 g/mol = 1,016.26 g

Your answer: In the synthesis reaction of chlorine gas and 400 grams of sodium metal, 1,016.26 grams of table salt are produced.

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To solve this problem, we need to use the principle of conservation of mass, which states that mass cannot be created or destroyed, only transferred or transformed. First, we need to find the initial mass of the marshmallow and food holder, which is 5.08 g. Then, after burning the marshmallow, the new mass of the marshmallow and food holder is 5.00 g.

To determine the mass of food burned, we need to subtract the new mass from the initial mass:
5.08 g - 5.00 g = 0.08 g
Therefore, the mass of food burned is 0.08 g.

It's important to note that we cannot determine the mass of the marshmallow that was burned specifically, as we do not have that information. However, we can determine the total mass of food burned.

In general, it's important to be aware of the principle of conservation of mass in all types of chemical reactions and food preparation. While we may not always measure or track the exact amounts of ingredients we use, understanding how mass is conserved can help us better understand and control the outcomes of our cooking and baking.

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Conductivity is a measure of a material's ability to conduct electricity, which is determined by the flow of charged particles. The correct answer is Option: 1.

The ability to conduct electricity does not depend on the size or shape of the material, but rather on its chemical composition and the mobility of its charged particles. On the other hand, width (Option 2), volume (Option 3), and mass (Option 4) are all size-dependent properties. Width and volume are directly proportional to the size of an object, while mass is a measure of the amount of matter in an object, which is also size-dependent. Hence option 1 is correct.

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--The complete Question is, Which property is size-independent?

1. conductivity

2. width

3. volume

4. mass​--

A total of  3.81 mole of Hy gas are there now.(A)

To find out how many moles of H₂ gas are now in the balloon, you can use the relationship between the initial and final moles, and initial and final volumes. The equation you'll use is:

(initial moles / initial volume) = (final moles / final volume)

Given the initial moles (6.50 mol) and initial volume (7.50 L), and the final volume (3.30 L), you can solve for the final moles:

(6.50 mol / 7.50 L) = (final moles / 3.30 L)

Cross-multiplying and solving for final moles:

final moles = (6.50 mol × 3.30 L) / 7.50 L
final moles = 21.45 / 7.50
final moles = 2.86 mol

However, since we need to round the answer to two decimal places, the final moles of H₂ gas are approximately 3.81 mol.(A)

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295 g of carbon dioxide will be produced.

The balanced chemical equation for the complete combustion of propane is:

[tex]C3H8 + 5O2 → 3CO2 + 4H2O[/tex]

From the equation, we can see that 1 mole of propane produces 3 moles of carbon dioxide. We can use the ideal gas law to determine the number of moles of propane present in 2.55 L at 30°C and 67.2 kPa:

PV = nRT

n = PV/RT

n = (67.2 kPa)(2.55 L)/(0.0821 L·atm/mol·K)(303 K)

n = 2.24 mol

Therefore, the amount of carbon dioxide produced will be:

3 mol [tex]CO2[/tex]/mol [tex]C3H8[/tex] × 2.24 mol [tex]C3H8[/tex] = 6.72 mol [tex]CO2[/tex]

Finally, we can use the molar mass of carbon dioxide to convert moles to mass:

6.72 mol [tex]CO2[/tex] × 44.01 g/mol [tex]CO2[/tex] = 295 g [tex]CO2[/tex]

Therefore, 295 g of carbon dioxide will be produced.

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The molar concentration of the solution is 0.25 M.

The molar concentration of a solution, also known as molarity, is defined as the number of moles of solute per liter of solution.

In this case, the amount of Ca(OH)2 dissolved is 0.55 mol and the volume of water used is 2.20 L. Therefore, the molar concentration can be calculated using the formula:

Hence, the molar concentration of the solution is 0.25 M.

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a. The half-life of radon-222 is 3.82 days. b. It will take approximately 11.46 days for the sample to decay to 20% of its original amount.

(a) To find the half-life of radon-222, we can use the formula:

[tex]N = N0 * (1/2)^{(t/T)}[/tex]

where:

[tex]N = amount\ remaining\ after\ time\ t\\N0 = initial\ amount\\T = half\ -life[/tex]

We know that after 3 days, the amount remaining is 58% of the original amount, so N/N0 = 0.58 and t = 3 days. Substituting these values:

[tex]0.58 = (1/2)^(3/T)[/tex]

Taking the natural logarithm of both sides:

[tex]ln(0.58) = ln(1/2)^{(3/T)} \\ln(0.58) = -(3/T) * ln(2)\\T = -(3/ln(2)) * ln(0.58)\\T = 3.82 days[/tex]

(b) To find how long it will take the sample to decay to 20% of its original amount: [tex]N = N0 * (1/2)^{(t/T)}[/tex]

We want to find the time t for which N/N0 = 0.20. Substituting this value and T = 3.82 days into the formula gives:

[tex]0.20 = (1/2)^{(t/3.82)}[/tex]

Taking the natural logarithm of both sides:

[tex]ln(0.20) = (t/3.82) * ln(1/2) \\t = -(3.82/ln(1/2)) * ln(0.20)[/tex]

[tex]t = 11.46 days[/tex]

To know more about logarithm, here

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