How to solve using the Ideal Gas Law

Question

As the result of a chemical reaction, 19.8 g of CO2 gas is produced. Using the ideal gas law, determine the volimn of gas produced when the pressure is 1.00 atmosphere and the temperature is 33.0^C.

Answer 1

Ideal gas law states that: PV = nRT, where P is the pressure of the gas, V is the volume taken up by the gas, T is the temperature of the gas, R is the gas constant, and n is the number of moles of the gas.

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Let's extract all the important information from the problem.

Given: Find:

P = 1 atm V

T = 33°C

mass = 19.8g CO₂

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Solving for V, we can transform the ideal gas law into the following:

V = nRT/P

We don't have n, but we can solve for it using the mass. We also need to make sure that all of our values are in the correct units.

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Solve for n.

We can go from mass to moles by dividing the mass by the molar mass of Carbon Dioxide.

The molar mass of Carbon Dioxide is found by adding the atomic masses of each of the constituents of carbon dioxide, carbon and oxygen.

(1) Use the periodic table to find the atomic masses of oxygen and carbon, which are 15.999 g/mol and 12.011 g/mol, respectively.

(2) Since 1 molecule of carbon dioxide (CO₂) is made up of 1 Carbon atom and 2 Oxygen atoms, the molar mass of CO₂ is as follows:

2(15.999 g/mol) + 12.011 g/mol = 31.998 g/mol + 12.011 g/mol = 44.01 g/mol CO₂

We can now divide by the mass of carbon by the molar mass to get n:

n = 19.8g CO₂ * 1 mol CO₂/44.01 g CO₂ = 0.45 mol CO₂

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Convert all units appropriately.

Since R = 0.082 L-atm/K-mol, the temperature must be in Kelvin.

K = °C + 273.16, so our temperature T = 306.15 K.

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Plug everything into the modified ideal gas equation:

V = nRT/P = (0.45 mol CO₂)(0.082 L-atm/K-mol)(306.15 K)/(1 atm) = 11.3 L

The volume of CO₂ gas produced is 11.3 L.