Chapter U3, Problem 15STP

Interpretation Introduction

Interpretation:

The statement that best describes the relationship between gas measurements needs to be determined.

Concept introduction:

The ideal gas equation can be represented as follows:

$PV=nRT$

Here, P is pressure, V is volume, n is number of moles, R is Universal gas constant and T is temperature.

Answer to Problem 15STP

Option (a) is correct.

Explanation of Solution

Reason for correct statement:

(a)

For an ideal gas equation, the pressure, volume, number of moles and temperature is related to each other as follows:

$PV=nRT$

Now, when temperature and number of moles are constant, the relation between volume and pressure can be represented as follows:

$PV=C$

Here, $C=nRT$

The above expression can be represented as follows:

$\begin{array}{l}P=\frac{C}{V}\\ P\propto \frac{1}{V}\end{array}$

Or, pressure of gas is inversely proportional to volume of the gas.

Thus, statement (a) is correct.

Conclusion

Reason for incorrect statement:

(b)

Now, when pressure and number of moles not change, the relation between volume and temperature can be represented as follows:

$\begin{array}{l}\frac{V}{T}=\frac{nR}{P}\\ =C\\ V=CT\\ V\propto T\end{array}$

Thus, volume is directly proportional to temperature and the given statement is incorrect.

(c)

Now, when number of moles of gas and volume not change, the relation between pressure and temperature can be represented as follows:

$\begin{array}{l}P=\frac{nR}{V}T\\ P=CT\\ P\propto T\end{array}$

Thus, P is directly proportional to T and the given statement is incorrect.

(d)

When temperature and pressure is not change, the relation between number of moles and volume is represented as follows:

$\begin{array}{l}V=n\frac{RT}{P}\\ V=Cn\\ V\propto n\end{array}$

Thus, volume is directly proportional to number of moles and the given statement is incorrect.