Question

In a certain town when the temperature was 27°C and the atmospheric pressure was 9900 Pa, a 300 cm³ container was sealed. The container, which contained only air, was placed into a refrigerator until its temperature cooled to 5°C. Calculate the new pressure in the container.

a) 10150 Pa
b) 9750 Pa
c) 9625 Pa
d) The calculation requires additional information.

Answer 1

After using the combined gas law, the final pressure in the container when cooled to 5°C is approximately 9175 Pa, which does not match any of the given options. Hence, the answer is that the calculation requires additional information. Option D is correct.

Step-by-step explanation:

The question involves using the combined gas law to calculate the new pressure in a sealed container due to a change in temperature. Since the question specifies that the container is sealed, the volume remains constant and the number of molecules in the container remains the same.

To find the new pressure after cooling the gas, we can use the combined gas law which shows the relationship between pressure, volume, and temperature:

P1/T1 = P2/T2

Where:

P1 is the initial pressure (9900 Pa)

T1 is the initial temperature in Kelvin (27°C + 273.15 = 300.15 K)

P2 is the final pressure (unknown)

T2 is the final temperature in Kelvin (5°C + 273.15 = 278.15 K)

Rearranging the formula to solve for P2 gives us:

P2 = P1 * (T2/T1)
Substitute the given values:
P2 = 9900 Pa * (278.15 K / 300.15 K)
Now by calculating:

P2 = 9900 Pa * 0.92676
P2 = 9174.924 Pa
Thus, the final pressure when rounded to the nearest whole number is 9175 Pa, which is not one of the presented options. Therefore, the correct answer is (d) The calculation requires additional information.