Answer :
Final answer:
To find the temperature at which the pressure would be 101.3 kPa if the volume remains constant, we use the pressure-temperature relationship from the combined gas law. After converting all units to SI units and plugging in the known values, we solve for the unknown temperature. The answer is approximately 91.11 Celsius, with the closest provided option being 100 degrees Celsius.
Explanation:
To determine at what temperature in Celsius the pressure would be 101.3 kPa if the volume remains constant, when a gas occupies a volume of 50 ml at 27 degrees Celsius and 630 mmHg, we need to use the combined gas law, focusing on the pressure-temperature relationship since the volume does not change. This relationship can be described by the formula:
P1/T1 = P2/T2, where P is pressure and T is temperature in Kelvins.
First, it's important to convert all units to SI units. The initial pressure P1 needs to be converted from mmHg to kPa, and the temperatures need to be converted from Celsius to Kelvins.
630 mmHg is equivalent to 840 mmHg / 101.3 kPa = 0.8302 kPa.
The initial temperature T1 in Kelvins is 27 °C + 273.15 = 300.15 K.
We are given the final pressure P2 as 101.3 kPa, and we need to find the final temperature T2 in Kelvins:
(630 mmHg / 101.3 kPa) / (27 °C + 273.15 K) = (101.3 kPa) / T2
Solving for T2 gives us:
T2 = (101.3 kPa × (300.15 K)) / (0.8302 kPa)
Calculating T2 yields approximately 364.26 K, which is 364.26 K - 273.15 = 91.11 °C
The closest answer among the provided options is (b) 100 degrees Celsius.
