Question

what will happen to the pressure of a gas if its absolute temperature triples (increases by a factor of three) while the number of moles of gas and the volume are held constant?
select the correct answer below:
the pressure will decrease by a factor of three.
the pressure will triple (increase by a factor of three).
the pressure will double (increase by a factor of two).
the pressure will be cut in half (decrease by a factor of two).

Explanation:

Step1: Recall the ideal gas law

$$PV = nRT$$
where \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles, \(R\) is the ideal gas constant, and \(T\) is absolute temperature.

Step2: Rearrange for pressure

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

Step3: Analyze the situation

Given \(n\), \(V\), and \(R\) are constant. Let initial pressure \(P_1=\frac{nR T_1}{V}\) and final temperature \(T_2 = 3T_1\). Then final pressure \(P_2=\frac{nR T_2}{V}=\frac{nR(3T_1)}{V}=3\times\frac{nR T_1}{V}=3P_1\). So pressure triples.

Answer:

The pressure will triple (increase by a factor of three).