A sample of gas at 42°C has a volume of 5.2 L and exerts a pressure of 1.00 atm. How many moles of gas are in the sample?
Use ideal gas law. PV=nRT.Solve for n and substitute R=0.08206 L-Atm/mol-K, T=(273+42)K=315K, V=5.2 L, P = 1.00 atm.
To find the number of moles of gas in the sample, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (in atm)
V = volume of the gas (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature of the gas (in Kelvin)
First, we need to convert the given temperature from Celsius to Kelvin. The formula to convert Celsius to Kelvin is:
K = °C + 273.15
So, the temperature in Kelvin would be:
T = 42 + 273.15 = 315.15 K
Now, we can substitute the given values into the ideal gas law equation:
1.00 atm * 5.2 L = n * 0.0821 L·atm/(mol·K) * 315.15 K
Simplifying the equation:
5.2 = n * 25.72
Dividing both sides by 25.72:
n = 5.2 / 25.72
n ≈ 0.202 moles
Therefore, there are approximately 0.202 moles of gas in the given sample.