Question

1. before we begin, make a prediction of what you think will happen to gas pressure when the temperature of the gas is increased. write your prediction down below include any rationale that you thought of when making your prediction.
2. a large beaker of isopropanol is cooled using crushed dry ice powder. the mixture cools to -40°c.
3. a sealed test tube containing gas has a temperature and pressure sensor sealed inside
4. the test tube is immersed in the liquid, and cooled to a temperature near -40°c
5. a heating plate is turned on, so the temperature of the liquid begins to increase
6. the pressure and temperature are displayed on the screen at right

Explanation:

The problem involves a gas in a sealed test tube, and we're predicting pressure - temperature relationship. According to the ideal gas law ($PV = nRT$), when the amount of gas ($n$) and volume ($V$) are constant (since the test tube is sealed, $n$ is fixed and the volume of the gas - containing space is fixed), pressure ($P$) and temperature ($T$) are directly proportional. So as the temperature of the gas increases (when the heating plate is on and the liquid's temperature rises, which will transfer heat to the gas), the pressure of the gas should also increase. The rationale is based on the ideal gas law, where with constant $n$ and $V$, $P\propto T$.

Answer:

Prediction: When the temperature of the gas is increased, the pressure of the gas will increase.
Rationale: By the ideal gas law $PV = nRT$, for a sealed test tube, the amount of gas ($n$) and the volume of the gas - occupied space ($V$) are constant. So pressure ($P$) is directly proportional to temperature ($T$) ($P=\frac{nR}{V}T$). As temperature ($T$) increases, pressure ($P$) will increase.