Question

Question #a773b

Answer 1

The volume of gas is 3.571 L.

Step 1. Write the balanced equation.

`"CaCO"_3 → "CaO + CO"_2`

Step 2. Calculate the moles of `"CO"_2`

`"Moles of CO"_2 = 15.74 cancel("g CaCO₃") × (1 cancel("mol CaCO₃"))/(100.09 cancel("g CaCO₃")) × ("1 mol CO"_2)/(1 cancel("mol CaCO₃")) = "0.157 26 mol CO"_2`

Step 3. Use the Ideal Gas Law to calculate the volume of CO₂

`PV = nRT`

`V = (nRT)/P`

STP is 100 kPa and 273.15 K.

`V = 0.157 26 cancel("mol") × (8.314 cancel("kPa")·"L" ·cancel("K⁻¹mol⁻¹") × 273.15 cancel("K"))/(100 cancel("kPa")) = "3.571 L"`

Answer 2

The great thing about STP is that the ideal gas law calculations have already been done for you for 1 mole of a gas.

At STP conditions, 100.0 kPa and 0 degrees C, to be more precise, 1 mole of any ideal gas occupies exactly 22.71 L. This is known as the molar volume of a gas at STP.

So, in your case, once you get the number of moles of carbon dioxide produced, you can multiply that value by the molar volume of a gas at STP to get the volume you need

`V = n * V_"molar" = 0.15726cancel("moles") * "22.71 L"/(1cancel("mol")) = "3.571 L"`

So, don't forget about the molar volume of a gas at STP. If nothing else, you can use it to double check the calculations you've made using the ideal gas law.

At STP, for n moles of ideal gas

`PV = nRT => V/n = underbrace((RT)/P)_(color(blue)("22.71 L"))`