What is the volume in liters of 3.2 moles methane gas, CH4, at 12degrees C and 1.52 atm?
Use PV = nRT
A sample of gas confined in a cylinder with a movable piston is kept at constant pressure. The volume of the gas doubles when the temperature of the gas is changed from
To find the volume of gas, we can use the Ideal Gas Law equation:
PV = nRT
where:
P = pressure
V = volume
n = moles of gas
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature in Kelvin
First, we need to convert the temperature from degrees Celsius to Kelvin:
T(K) = T(C) + 273.15
T(K) = 12 + 273.15
T(K) = 285.15 K
Now we can substitute the values into the equation and solve for the volume:
(1.52 atm) * V = (3.2 moles) * (0.0821 L.atm/mol.K) * (285.15 K)
Let's solve the equation step-by-step:
Step 1: Multiply the number of moles by the ideal gas constant and the temperature in Kelvin.
(3.2 moles) * (0.0821 L.atm/mol.K) * (285.15 K) = 6.700992 L.atm
Step 2: Divide both sides of the equation by the pressure to isolate the volume.
V = (6.700992 L.atm) / (1.52 atm)
Step 3: Simplify the equation.
V ≈ 4.40701 L
Therefore, the volume of 3.2 moles of methane gas at 12 degrees Celsius and 1.52 atm is approximately 4.40701 liters.
To find the volume of 3.2 moles of methane gas at a given temperature and pressure, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's convert the temperature from degrees Celsius to Kelvin. To do this, we add 273.15 to the given temperature:
T = 12°C + 273.15 = 285.15 K
Next, we need to convert the pressure from atm to units of pressure that correspond to the units of the ideal gas constant. The ideal gas constant, R, has different values depending on the units used for pressure. In this case, R is typically expressed in units of (L·atm)/(mol·K). Since the given pressure is already in atm, we can use the ideal gas constant as it is.
Now, we can rearrange the ideal gas law equation to solve for V:
V = (nRT) / P
Substituting the given values into the equation:
V = (3.2 moles) * ( (0.0821 L·atm)/(mol·K) ) * (285.15 K) / (1.52 atm)
Calculating this expression gives us the volume in liters:
V ≈ 168.76 liters
So, the volume of 3.2 moles of methane gas at 12 degrees Celsius and 1.52 atm is approximately 168.76 liters.