Question

10.0 moles of carbon dioxide gas has volume of 245L. If 5.0 moles of the carbon dioxide is removed at the same temperature and pressure, what volume will gas now occupy?

Answer 1

Question #73416

Answer:

Conditions: constant temperature and pressure

$$\begin{array}{l} n_1 = \text{initial moles of gas} = 10 \text{ mol} \\ V_1 = \text{initial volume of gas} = 245 \text{ L} \end{array}$$

moles gas removed = 5 mol

$$\begin{array}{l} n_2 = \text{initial moles gas} - \text{moles gas removed} \\ n_2 = 10 - 5 = 5 \text{ mol} \end{array}$$ $$\begin{array}{l} \frac{V_1}{n_1} = \frac{V_2}{n_2} \\ V_2 = \frac{V_1}{n_1} \times n_2 \\ = \frac{245}{10} \times 5 \end{array}$$

When some of this gas is removed while the temperature is held constant, the pressure should drop because there will be fewer collisions between the gas molecules and the container walls.

BUT, we have been told that the pressure remains constant, therefore the volume of the gas must decrease in order to maintain the same pressure $V_2 = 122.5$ L

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