Question in Chemistry

Question

Sodium metal reacts with water to produce hydrogen gas according to the following equation:

2Na(s) + 2H₂O(l)2NaOH(aq) + H₂(g)

The product gas, H₂, is collected over water at a temperature of 25 °C and a pressure of 758 mm Hg. If the wet H₂ gas formed occupies a volume of 6.32 L, the number of grams of H₂ formed is______________ g. The vapor pressure of water is 23.8 mm Hg at 25 °C

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Calcium carbide reacts with water to produce acetylene gas according to the following equation:

CaC₂(s) + 2H₂O(l)C₂H₂(g) + Ca(OH)₂(aq)

The product gas, C₂H₂, is collected over water at a temperature of 25 °C and a pressure of 748 mm Hg. If the wet C₂H₂ gas formed occupies a volume of 7.76 L, the number of moles of CaC₂ reacted was _______________ mol. The vapor pressure of water is 23.8 mm Hg at 25 °C.

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Answer 1

To answer this question we will need to use the ideal gas law (P is pressure, V volume, n moles, R ideal gas constant, T temperature),

PV=nRT

and Dalton's law of partial pressures, which tells us the total pressure is the sum of the partial pressures of the gases making up a mixture. In this case the mixture is H2, the gas you are collecting, and water vapor H2O. Every liquid has a vapor pressure, there will be some molecules in the gas phase exerting a pressure.

P(total) = P(H2O) + P(H2)

We want the partial pressure of the H2, not the total pressure.

P(H2) = P(total) - P(H2O) = 758 mmHg - 23.8 mmHg = 734.2 mmHg

This is the pressure we are going to plug into the ideal gas law equation, but when we do plug it in we want to make sure units cancel out. So the units we use for pressure, temperature, and volume must match the units of the ideal gas constant R. R = 0.08206 L atm / mol K, so I am going to convert the pressure from mmHg to atm.

734.2 mmH x 1 atm/760 mmHg = 0.9661 atm

We'll also need to convert the temperature to Kelvin.

25 C + 273 = 298 K

Now let's take the ideal gas law, and solve for n, the number of moles.

n = PV/RT

Time to plug everything in.

n = (0.9661 atm x 6.32 L)/(0.08206 L atm/mol K x 298 K) = 0.2497 mol

But we weren't asked for the amount in moles, we were asked for the mass. So we need the molar mass of H2.

mass = molar mass x number of moles

mass = 0.2497 mol x 2.01568 g/mol = 0.5033 g of H2

Now for the second problem. This will look a lot like the first problem. First we have to get the partial pressure of the acetylene gas.

P(C2H2) = 748 mmHg - 23.8 mmHg = 724.2 mmHg

Convert it to atm.

724.2 mmHg x 1 atm/760 mmHg = 0.9529 atm

Solve for n and plug it all in.

n = PV/RT = (0.9529 atm x 7.76 L)/(0.08206 L atm/mol K x 298 K) = 0.3024 mol C2H2

But we are interested in the number of moles of the reactant CaC2. So we need to look at the coefficients in the balanced equation to figure out the ratio they react and form at.

0.3024 mol C2H3 x 1 mol CaC2/1 mol C2H2 = 0.3024 mol CaC2

The react in a 1:1 ratio. We should also make sure our answers have the correct number of significant figures, which should be no more than the number of significant figures in the numbers provided in the problem. So the solutions should actually be 0.503 g H2 and 0.302 mol CaC2.