Question
How many mol of CH_{4 }are in a L tank exerting a pressure of atm when the temperature is degrees Celsius?
How many mol of CH_{4 }are in a L tank exerting a pressure of atm when the temperature is degrees Celsius?
In this example there is an implicit assumption that methane, CH_{4 }, is a gas. In the problem all of the data, pressure, temperature and volume, refer to physical properties of the gas. If there was information indicating the gas was interacting with another substance, as in a chemical reaction, we would need to use a different strategy.
Factoid:
The only time we see information about pressure associated with a phase other than gas is when discussing vapor pressure. Vapor pressure is associated with liquids, and is a measure of the pressure exerted by the vapor above a liquid at a given temperature.
Factoid:
Any problem containing combinations of data including pressure, temperature, volume, mol, density and/or mass of a gas requires the use of the Ideal Gas Equation.
Problem Solving Strategy:
Since this is a problem about a gas, and all the data provided are physical properties we conclude it is an Ideal Gas Law Problem and we need to construct a table to associate values in the problem statement with the variables in the Ideal Gas Law (PV = nRT).
The Table before entering the data would look like;
V 
n 
R 
T 
Condition 

1 
Completing the table with the data from the problem;
V 
n 
R 
T 
Condition 

atm 
? 
0.0821 L atm mol^{1} K^{1} 
C 
1 
Notice there is only one condition for this gas. Before continuing we must convert all the units for each variable so they correspond to the units for R. THe units on pressure and volume agree with the units in R, but not the units on temperature. Temperature units must be Kelvins in any Ideal Gas Law Problem.
Converting degrees Celsius to Kelvins;
K = 273.15 + degrees Celsius
K = 273 + =
So the table would now look like;
V 
n 
R 
T 
Condition 

atm 
? 
0.0821 L atm mol^{1} K^{1} 
K 
1 
Now substitute the values for each variable into the Ideal Gas Equation;
PV = nRT
Substituting;
(atm ) ( L) = n (0.0821 L atm mol^{1} K^{1}) ( K)
Solving for the unknown, n, in the problem;
mol CH_{4 }
Summary:
1. Recognize the problem as Ideal Gas Law Problem. To help recognize the problem we note the substance is referred to as a gas either implicitly or explicitly and any information in the problem are physical properties of the substance, i.e., pressure, volume, temperature,mol, density, or mass of the gas.
2. Recognize the problem has only one condition, it is a single variable problem.
3. Write the Ideal Gas Equation; PV = nRT
4. Construct a table and assign a value from the problem statement to each of the variables in the Ideal Gas Equation.
5. Convert units of each variable intot he units corresponding to the value of R; 0.0821 L atm mol^{1} K^{1}
6. Substitute the values into the equation and solve for the unknown.
Help Me!
How many mol of CH_{4 }are in a L tank exerting a pressure of atm when the temperature is degrees Celsius?
Summary:
1. Recognize the problem as Ideal Gas Law Problem. To help recognize the problem we note the substance is referred to as a gas either implicitly or explicitly and any information in the problem are physical properties of the substance, i.e., pressure, volume, temperature,mol, density, or mass of the gas.
2. Recognize the problem has only one condition, it is a single variable problem.
3. Write the Ideal Gas Equation; PV = nRT
4. Construct a table and assign a value from the problem statement to each of the variables in the Ideal Gas Equation.
5. Convert units of each variable intot he units corresponding to the value of R; 0.0821 L atm mol^{1} K^{1}
6. Substitute the values into the equation and solve for the unknown.