# A flexible container holds "6.70 mol" of a gas. An additional "3.50 mol" of the gas is added to the container until it reaches a final volume of "25.4 L" while temperature and pressure are kept constant, what was the initial volume?

Nov 5, 2016

The initial volume was 16.7 L.

#### Explanation:

This problem requires Avogadro's law, which states that the amount (moles) of a gas is directly proportional to its volume, such that if the amount increases, the volume increases and vice versa. You correctly determined the formula to use: ${V}_{1} / {n}_{1} = {V}_{2} / {n}_{2}$

Known
${n}_{1} = \text{6.70 mol}$
${V}_{2} = \text{25.4 L}$
${n}_{2} = \text{6.70 mol+3.50 mol"="10.2 mol}$

Unknown
${V}_{1}$

Solution
Rearrange the equation to isolate ${V}_{1}$. Substitute the known values into the equation and solve.

${V}_{1} = \frac{{V}_{2} {n}_{1}}{n} _ 2$

V_1=(25.4"L"xx6.70cancel"mol")/(10.2cancel"mol")="16.7 L" rounded to three significant figures