3.25 moles of gas take up 40.0 l of space under constant pressure and temperature conditions. what volume is…

3.25 moles of gas take up 40.0 l of space under constant pressure and temperature conditions. what volume is required to hold 1.25 moles of the gas? v₂ = ? l

3.25 moles of gas take up 40.0 l of space under constant pressure and temperature conditions. what volume is required to hold 1.25 moles of the gas? v₂ = ? l

Answer

Explanation:

Step1: Set up the proportion

At constant pressure and temperature, the volume of a gas is directly proportional to the number of moles. So we have the proportion $\frac{V_1}{n_1}=\frac{V_2}{n_2}$, where $V_1 = 40.0$ L, $n_1=3.25$ moles, and $n_2 = 1.25$ moles.

Step2: Solve for $V_2$

Cross - multiply the proportion: $V_2=\frac{V_1\times n_2}{n_1}$. Substitute the given values: $V_2=\frac{40.0\times1.25}{3.25}$. $V_2=\frac{50}{3.25}=\frac{50\times4}{3.25\times4}=\frac{200}{13}\approx 15.4$ L

Answer:

$15.4$