Question

part b a sample of gas in a cylinder as in the example in part a has an initial volume of 70.0 l, and you have determined that it contains 1.30 moles of gas. the next day you notice that some of the gas has leaked out. the pressure and temperature remain the same, but the volume has changed to 17.5 l. how many moles of gas (n₂) remain in the cylinder? express your answer with the appropriate units. view available hint(s) n₂ = 1.46 mol submit previous answers incorrect; try again; 5 attempts remaining

Explanation:

Step1: Identify the gas law

Since pressure (\(P\)) and temperature (\(T\)) are constant, we use Avogadro's law, which states \(\frac{V_1}{n_1}=\frac{V_2}{n_2}\). Here, \(V_1 = 70.0\space L\), \(n_1 = 1.30\space mol\), \(V_2 = 17.5\space L\).

Step2: Rearrange the formula

Rearrange Avogadro's law to solve for \(n_2\): \(n_2=\frac{V_2\times n_1}{V_1}\).

Step3: Substitute the values

Substitute \(V_1 = 70.0\space L\), \(n_1 = 1.30\space mol\), \(V_2 = 17.5\space L\) into the formula: \(n_2=\frac{17.5\space L\times1.30\space mol}{70.0\space L}\).

Step4: Calculate the result

First, calculate the numerator: \(17.5\times1.30 = 22.75\). Then divide by the denominator: \(\frac{22.75}{70.0}=0.325\space mol\).

Answer:

\(0.325\space mol\)