Asked by Vansh Agarwal on May 20, 2024
Verified
At what temperature is a 5.0 L container of 4.0 g of hydrogen gas at 15.0 atm, assuming it obeys the ideal gas law?
A) 25.0°C
B) 184°C
C) 456°C
D) 75.0°C
Ideal Gas Law
A fundamental equation that relates pressure, volume, temperature, and the amount of gas, represented as PV = nRT.
Hydrogen Gas
A colorless, odorless, highly flammable gas, the lightest of all gases, used in various industrial processes.
Temperature
An indicator of how hot or cold a system is, determined by the mean kinetic energy of its particles.
- Understand and apply the ideal gas law to solve problems related to the temperature, pressure, and volume of a gas.
Verified Answer
LN
Loren NeversMay 21, 2024
Final Answer :
B
Explanation :
To find the temperature, we use the ideal gas law equation: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/(mol·K)), and T is temperature in Kelvin. First, calculate the number of moles of hydrogen gas (H2) using its molar mass (2.02 g/mol): n = 4.0 g / 2.02 g/mol = 1.98 mol. Then, rearrange the ideal gas law to solve for T: T = PV / (nR). Substituting the given values and converting the temperature to Celsius: T = (15.0 atm * 5.0 L) / (1.98 mol * 0.0821 L·atm/(mol·K)) = 457.3 K. Converting to Celsius: 457.3 K - 273.15 = 184.15°C, which rounds to 184°C.
Learning Objectives
- Understand and apply the ideal gas law to solve problems related to the temperature, pressure, and volume of a gas.