How to Calculate Temperature of a Gas in a Balloon?
What are the given values in the problem?
A gas fills a balloon with a volume of 1.20 L under a pressure of 0.998 atm. The amount of gas present is 0.047 mol. What is the temperature of the gas?
What are the options for the temperature of the gas?
A. 0 K
B. 207 K
C. 107 K
D. 307 K
Answer:
The correct temperature of the gas in the balloon is 307 K.
In the problem given, we have the volume of the balloon, the pressure of the gas, and the amount of gas present. To calculate the temperature of the gas, we can use the ideal gas law equation:
PV = nRT
where:
P = pressure of the gas (atm)
V = volume of the gas (L)
n = amount of gas (mol)
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature of the gas (K)
Plugging in the given values:
0.998 atm * 1.20 L = 0.047 mol * (0.0821 L.atm/mol.K) * T
Solving for T:
T = (0.998 atm * 1.20 L) / (0.047 mol * 0.0821 L.atm/mol.K)
T = 306.86 K
Therefore, the temperature of the gas in the balloon is approximately 307 K.