Question

The gases in a hair spray can are at a temperature of 27°C and a pressure of 30 mmHg. If the gases in the can reach a pressure of 90 mmHg, the can will explode. To what temperature must the gases be raised in order for the can to explode? Assume constant volume.

Answer 1

To prevent the hair spray can from exploding at a pressure of 90 mmHg, the temperature of the gases inside the can must not exceed 627.3°C, as per Gay-Lussac's Law.

Step-by-step explanation:

The student is asking about the relationship between the temperature and pressure of the gases inside a hair spray can, assuming a constant volume. This scenario is guided by the gas laws, specifically Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its temperature when volume is held constant.

To find out to what temperature the gases must be raised for the can to explode at a pressure of 90 mmHg, we can set up a proportion using the initial conditions (temperature = 27°C, pressure = 30 mmHg) and solve for the final temperature. First, we convert the Celsius temperatures to Kelvin by adding 273.15. Then we apply Gay-Lussac's Law (P1/T1 = P2/T2) to find the final temperature (T2) when the pressure is 90 mmHg.

Using the values:

• P1 = 30 mmHg
• T1 = 27°C + 273.15 = 300.15 K
• P2 = 90 mmHg

We rearrange the law to solve for T2:

T2 = (P2 × T1) / P1 = (90 mmHg × 300.15 K) / 30 mmHg = 900.45 K

Finally, we convert this back to Celsius: T2 = 900.45 K - 273.15 = 627.3°C

This is the temperature to which the gas must be raised for the can to potentially explode.