How many moles of hydrogen H2,
gas are contained in a volume of 2L
at 280K
and 1.5atm
The Correct Answer and Explanation is:
To calculate how many moles of hydrogen gas (H₂) are contained in a gas sample, we can use the Ideal Gas Law:PV=nRTPV = nRTPV=nRT
Where:
- PPP = pressure (in atmospheres, atm)
- VVV = volume (in liters, L)
- nnn = number of moles (what we are solving for)
- RRR = ideal gas constant = 0.0821 L·atm/mol·K
- TTT = temperature (in Kelvin, K)
Step 1: Interpret the question
We are told:
- Volume V=2V = 2V=2 liters
- Temperature T=280T = 280T=280 Kelvin
- Pressure P=1.5P = 1.5P=1.5 atm
We need to solve for the number of moles nnn.
Step 2: Rearranging the ideal gas law
n=PVRTn = \frac{PV}{RT}n=RTPV
Substitute the known values:n=(1.5 atm)⋅(2 L)0.0821 L\cdotpatm/mol\cdotpK⋅280 Kn = \frac{(1.5\ \text{atm}) \cdot (2\ \text{L})}{0.0821\ \text{L·atm/mol·K} \cdot 280\ \text{K}}n=0.0821 L\cdotpatm/mol\cdotpK⋅280 K(1.5 atm)⋅(2 L)n=3.022.988n = \frac{3.0}{22.988}n=22.9883.0n≈0.1305 moln \approx 0.1305\ \text{mol}n≈0.1305 mol
Final Answer:
Approximately 0.131 moles of hydrogen gas are contained in the sample.
Explanation
The number of gas particles in a sample is usually measured in moles, which helps chemists relate macroscopic quantities to microscopic particles. To find the number of moles of a gas under certain conditions, the ideal gas law is a reliable formula as long as the gas behaves ideally, which hydrogen generally does under standard conditions.
In this case, we were given the volume, temperature, and pressure, and we wanted to find how many moles of hydrogen gas were present. The ideal gas law, expressed as PV=nRTPV = nRTPV=nRT, is rearranged to solve for moles: n=PV/RTn = PV / RTn=PV/RT. Each variable must be in the proper unit. Pressure should be in atmospheres, volume in liters, and temperature in Kelvin. The gas constant RRR is always 0.0821 L·atm/mol·K when using these units.
Plugging in the numbers, we got a pressure of 1.5 atm, a volume of 2 liters, and a temperature of 280 K. The formula gave us the result of about 0.131 moles of hydrogen gas. This value tells us how many “chemical packages” of hydrogen molecules are in the container under the specified conditions.
Understanding this principle is essential in chemistry, especially in reactions involving gases. By using the ideal gas law, we can predict and quantify how gases behave and how much of them is involved in reactions or processes like combustion, respiration, or industrial synthesis.
