Question

question
what will be the volume occupied by 2.5 moles of nitrogen gas exerting 1.75 atm of pressure at 475k?
select the correct answer below:
56 l
39 l
17 l
1.5 l

Explanation:

Step1: Recall the ideal gas law

$$PV = nRT$$
where \(P\) is pressure (\(1.75\) atm), \(n\) is moles (\(2.5\) mol), \(R\) is the ideal gas constant (\(0.0821\ L\cdot atm/(mol\cdot K)\)), and \(T\) is temperature (\(475\) K). We need to solve for \(V\).

Step2: Rearrange the ideal gas law for \(V\)

$$V=\frac{nRT}{P}$$

Step3: Substitute the values into the formula

$$V=\frac{2.5\ mol\times0.0821\ L\cdot atm/(mol\cdot K)\times475\ K}{1.75\ atm}$$
First, calculate the numerator: \(2.5\times0.0821\times475 = 2.5\times38.9975=97.49375\)
Then divide by the denominator: \(\frac{97.49375}{1.75}\approx55.71\approx56\ L\)

Answer:

56 L