Question

a flexible container holding 1.25 moles of a gas contracts from 25.0 l to 10.0 l when some gas is removed. the pressure and temperature remain the same throughout. how many moles of gas are in the contracted container? n₂ = ? mol

Explanation:

Step1: Identify the gas law

Since pressure (\(P\)) and temperature (\(T\)) are constant, we use Avogadro's Law, which states that \(\frac{V_1}{n_1}=\frac{V_2}{n_2}\) (where \(V\) is volume and \(n\) is moles of gas).

Step2: List known values

We know \(n_1 = 1.25\) mol, \(V_1 = 25.0\) L, \(V_2 = 10.0\) L, and we need to find \(n_2\).

Step3: Rearrange the formula to solve for \(n_2\)

From \(\frac{V_1}{n_1}=\frac{V_2}{n_2}\), we can rearrange to \(n_2=\frac{V_2\times n_1}{V_1}\).

Step4: Substitute the values into the formula

Substitute \(V_2 = 10.0\) L, \(n_1 = 1.25\) mol, and \(V_1 = 25.0\) L into the formula:
\(n_2=\frac{10.0\space L\times1.25\space mol}{25.0\space L}\)

Step5: Calculate the result

First, calculate the numerator: \(10.0\times1.25 = 12.5\) (L·mol). Then divide by the denominator: \(\frac{12.5\space L·mol}{25.0\space L}= 0.5\) mol.

Answer:

\(0.5\)