Question

Two gas samples have the same number of molecules, the same volume, and the same pressure. Which of the following could be true? A. The first gas sample has a temperature of 273 K, and the second gas sample has a temperature of 0o C. B. The first gas sample has a temperature of 273 K, and the second gas sample has a temperature of 298 K. C. The first gas sample has a temperature of 273 K, and the second gas sample has a temperature of 273o C. D. The first gas sample has a temperature of 273 K, and the second gas sample has a temperature of 100o C.

Answer 1

the correct answer is (A): The first gas sample has a temperature of 273 K, and the second gas sample has a temperature of 0 C.

Answer 2

Lets name one gas sample as A and other gas sample as B.
we can apply ideal gas law equation for both samples
PV = nRT
P - Pressure of A = Pressure of B
V - volume of A = volume of B
n - number of molecules of both A and B being equal is equivalent to number of moles of A = number of moles of B
R - universal gas constant
Tᵃ - temperature of A
Tᵇ - temperature of B
for gas A
PV = nRTᵃ --1)
for gas B
PV = nRTᵇ ---2)
when we divide both equations
1 = Tᵃ / Tᵇ
Tᵃ = Tᵇ
both temperatures are equal
temperature in Celsius + 273 = temperature in Kelvin
therefore 0 °C = 273 K
the correct answer is
A)
The first gas sample has a temperature of 273 K, and the second gas sample has a temperature of 0 °C