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Question

At constant volume, the pressure (P) of an ideal gas varies directly with its temperature (T). Initially, the gas pressure was 2.1 atm at a temperature of 273 K. What was the gas pressure when the temperature was 300 K? Round answer to 2 decimal places.

Answer 1

According to Charles's Law for ideal gases, at constant volume, the pressure is directly proportional to the temperature. The equation for this relationship is \(P_1/T_1 = P_2/T_2\), where \(P_1\) and \(T_1\) are the initial pressure and temperature, and \(P_2\) and \(T_2\) are the final pressure and temperature.

Let's use the given values:

\(P_1 = 2.1 \, \text{atm}\) at \(T_1 = 273 \, \text{K}\)

\(T_2 = 300 \, \text{K}\) (final temperature)

Now, rearrange the formula to solve for \(P_2\):

\[P_2 = \frac{P_1 \cdot T_2}{T_1}\]

Plug in the values:

\[P_2 = \frac{2.1 \times 300}{273}\]

Calculate this expression to find the gas pressure when the temperature is 300 K. Round the answer to 2 decimal places.

Answer 2

The general gas law is PV=nRT...which shows that as the problem states, pressure varies directly as absolute temperature.

2.1:P = 273:300 or P/2.1=300/273

P=2.1*300/273