Question

a sample of 6.25 mol of methane gas is trapped inside a cylinder with a movable piston. the initial volume of the cylinder is 1.25 l. without changing the temperature or pressure, an additional 8.85 mol of hydrogen gas are added to the cylinder causing the piston to move and the volume to expand. what is the new volume? 0.508 l 76.8 l 1.77 l 3.02 l

Explanation:

Step1: Determine the formula

Use Avogadro's law: $\frac{V_1}{n_1}=\frac{V_2}{n_2}$, where $V_1$ is the initial volume, $n_1$ is the initial number of moles, $V_2$ is the final volume, and $n_2$ is the final number of moles.

Step2: Identify the values

$V_1 = 1.25$ L, $n_1=6.25$ mol, $n_2=(6.25 + 8.85)$ mol $=15.1$ mol.

Step3: Solve for $V_2$

Rearrange the formula to $V_2=\frac{V_1\times n_2}{n_1}$.
Substitute the values: $V_2=\frac{1.25\times15.1}{6.25}$.
Calculate: $V_2 = 3.02$ L.

Answer:

3.02 L