Question

How many grams of CO2 are contained in 22.4 L of CO2 gas at STP?

Answer 1

Answer on Question #80442 – Chemistry – Other

Task:

How many grams of $\mathrm{CO}_{2}$ are contained in 22.4 L of $\mathrm{CO}_{2}$ gas at STP?

Solution:

Standard temperature at STP is zero degrees Celsius (273.15 K) and pressure of the gas at STP is 1 atmosphere (101 kPa).

$$R = 8.314 \, \mathrm{J} \cdot \mathrm{K}^{-1} \cdot \mathrm{mol}^{-1} = 0.0821 \, \mathrm{L} \cdot \mathrm{atm} \cdot \mathrm{K}^{-1} \cdot \mathrm{mol}^{-1}.$$

So if the gas in question happens to be at STP then the calculation would be:

$\mathrm{PV} = \mathrm{nRT}$, where $\mathrm{P}$ is pressure, $\mathrm{V}$ is volume, $\mathrm{T}$ is temperature in Kelvin and $\mathrm{R}$ is the ideal gas constant.

$$n = \mathrm{m} / \mathrm{M};$$ $$\mathrm{M}(\mathrm{CO}_{2}) = \mathrm{Ar}(\mathrm{C}) + 2 \cdot \mathrm{Ar}(\mathrm{O}) = 12 + 2 \cdot 16 = 44 \, \mathrm{g/mol}$$

Then,

$$pV = \frac{m}{M} RT;$$ $$pVM = mRT;$$ $$m = \frac{pVM}{RT};$$ $$m = \frac{1 \cdot 22.4 \cdot 44}{0.0821 \cdot 273.15} = 43.95 \, \mathrm{g}$$

Answer: 43.95 grams of $\mathrm{CO}_{2}$.

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