Question

The label on an aluminum aerosol can warns that the temperature should not exceed 50.0 °C. If a can is filled with an ideal gas at 505 kPa at 20.0 °C initially, what is the pressure (in atm) at 50.0 °C?

Answer 1

To calculate the new pressure at 50.0 °C when initially at 20.0 °C and 505 kPa, use Gay-Lussac's law, convert Celsius to Kelvin, apply the formula, and convert kPa to atm. The pressure at 50.0 °C is approximately 5.48 atm.

Step-by-step explanation:

The question involves calculating the pressure of a gas at a different temperature while assuming the volume and the amount of gas remain constant. To find the new pressure at 50.0 °C for a can initially at 20.0 °C and 505 kPa, one can use the ideal gas law in the form of Gay-Lussac's law, which states that the pressure of a gas is directly proportional to its temperature when volume and the amount of gas are kept constant (P1/T1 = P2/T2).

First, we need to convert the temperatures from Celsius to Kelvin:

• T1 = 20.0 °C = 293.15 K
• T2 = 50.0 °C = 323.15 K

Next, we apply Gay-Lussac's law:

P1 / T1 = P2 / T2

505 kPa / 293.15 K = P2 / 323.15 K

P2 = (505 kPa × 323.15 K) / 293.15 K

P2 = 554.96 kPa

To convert kPa to atm, we use the conversion factor 1 atm = 101.325 kPa. Therefore:

P2 in atm = 554.96 kPa / 101.325 kPa/atm

P2 in atm ≈ 5.48 atm

This is the pressure inside the can at 50.0 °C.

Answer 2

The new pressure in the can at 50.0 °C would be approximately 6.923 atm.

Step-by-step explanation:

To find the new pressure in the can, we can use the combined gas law equation:

P1V1/T1 = P2V2/T2

Where P1 and T1 are the initial pressure and temperature, P2 is the final pressure, T2 is the final temperature, and V1 and V2 are the initial and final volumes (assuming the volume remains constant in this case).

Using the given values, we can rearrange the equation to solve for P2:

P2 = (P1 * T2) / T1

Substituting the values:

P2 = (360 kPa * (50.0 °C + 273.15)) / (24 °C + 273.15)

P2 ≈ 700.8 kPa

Converting the pressure to atm:

P2 ≈ 700.8 kPa * 0.009869 atm/kPa ≈ 6.923 atm