A 2.01mol sample of nitrogen gas, stored in a container at 7.01°C, exerts a pressure of 76.1atm. Calculate the volume of nitrogen gas in the container. Round your answer to 3 significant figures.Note: Reference the Fundamental constants table for additional information.
Question
A 2.01mol sample of nitrogen gas, stored in a container at 7.01°C, exerts a pressure of 76.1atm. Calculate the volume of nitrogen gas in the container. Round your answer to 3 significant figures.Note: Reference the Fundamental constants table for additional information.
Solution
To solve this problem, we can use the ideal gas law equation, which is PV = nRT.
Here, P = pressure = 76.1 atm n = number of moles = 2.01 mol R = ideal gas constant. Since the pressure is given in atm, we will use the value of R = 0.0821 L.atm/(mol.K) T = temperature. This needs to be in Kelvin. To convert from Celsius to Kelvin, we add 273.15 to the Celsius temperature. So, T = 7.01°C + 273.15 = 280.16 K
We need to solve for V, the volume. Rearranging the ideal gas law equation to solve for V gives us V = nRT/P.
Substituting the given values into this equation gives us V = (2.01 mol * 0.0821 L.atm/(mol.K) * 280.16 K) / 76.1 atm.
Calculating this gives us V = 5.77 L.
So, the volume of the nitrogen gas in the container is 5.77 L.
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