Question

context
a leak causes a decrease in the amount of gas (moles) and therefore a decrease in volume when pressure and temperature are constant.
part b
a sample of gas in a cylinder as in the example in part a has an initial volume of 17.5 l. the next day you notice that some of the gas has leaked out. the pressure and temperature remain the same, but the volume is 11.75 l. how many moles of gas (n) remain in the cylinder?
express your answer with the appropriate units.
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n2 =
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Explanation:

Step1: Identify the gas law

Since temperature and pressure are constant, we use Avogadro's Law, which states that \(\frac{V_1}{n_1}=\frac{V_2}{n_2}\) (at constant \(T\) and \(P\)). But wait, actually, from the context, maybe Part A had initial conditions. Wait, the problem says "the sample in Part A has an initial volume of 37.1 L, and you have determined that it contains 3.10 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 is 17.5 L. How many moles of gas (n₂) remain?"

So initial \(V_1 = 37.1\) L, \(n_1 = 3.10\) mol, \(V_2 = 17.5\) L, find \(n_2\).

Using Avogadro's Law: \(\frac{V_1}{n_1}=\frac{V_2}{n_2}\) → \(n_2=\frac{V_2\times n_1}{V_1}\)

Step2: Plug in the values

\(V_1 = 37.1\) L, \(n_1 = 3.10\) mol, \(V_2 = 17.5\) L

\(n_2=\frac{17.5\space L\times3.10\space mol}{37.1\space L}\)

Calculate numerator: \(17.5\times3.10 = 54.25\)

Denominator: \(37.1\)

Then \(n_2=\frac{54.25}{37.1}\approx1.46\) mol

Answer:

\(n_2\approx\boxed{1.46}\) mol (Note: If more precise calculation: \(54.25\div37.1 = 1.46226...\approx1.46\) mol)