A 1.00 L sample of a pure gas weighs 0.785 g and is at 733.4 torr and 29.2 degree celcius.
a) what is the molar mass of the gas?
b) if the volume of the temperature are kept constant while 0.400 g of the same gas are added to that already in the container, what will the new pressure be?
Lauren, I showed you how to solve both parts of this problem. The only thing I didn't do was to do the math and I'm not going to do the math for you. I will help you through it if you are explicit about what you don't understand. And note that you are still spelling celsius incorrectly.
To calculate the molar mass of the gas in question, we can use the ideal gas law equation:
PV = nRT
Where:
- P is the pressure in atm
- V is the volume in liters
- n is the number of moles of gas
- R is the ideal gas constant (0.0821 L.atm/mol.K)
- T is the temperature in Kelvin
Let's convert the given values to appropriate units and rearrange the formula to solve for n:
P = 733.4 torr = (733.4 torr)(1 atm/760 torr) = 0.9658 atm
V = 1.00 L
T = 29.2 °C = (29.2 + 273.15) K = 302.35 K
R = 0.0821 L.atm/mol.K
0.9658 atm * 1.00 L = n * 0.0821 L.atm/mol.K * 302.35 K
Simplifying the equation:
0.9658 = n * 24.812635
Now solve for n:
n = 0.9658 / 24.812635 = 0.03898 mol
Next, we can calculate the molar mass (M) of the gas by dividing the mass of the gas by the number of moles:
Mass = 0.785 g
M = Mass / n
M = 0.785 g / 0.03898 mol = 20.12 g/mol
Therefore, the molar mass of the gas is 20.12 g/mol.
Now let's move on to the second part of the question.
The volume and temperature are held constant, so we can use the combined gas law to determine the new pressure:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
- P1 and P2 are the initial and final pressures, respectively
- V1 and V2 are the initial and final volumes, respectively
- T1 and T2 are the initial and final temperatures, respectively
We know:
P1 = 0.9658 atm (from part a)
V1 = 1.00 L (from part a)
T1 = 29.2 °C = 302.35 K (from part a)
P2 = ?
V2 = 1.00 L (constant volume)
T2 = remains the same (since only mass is added, not changing temperature)
Rearrange the equation to solve for P2:
P2 = (P1 * V1 * T2) / (V2 * T1)
Substituting the given values:
P2 = (0.9658 atm * 1.00 L * 302.35 K) / (1.00 L * 302.35 K)
Simplifying the expression:
P2 = 0.9658 atm
Therefore, the new pressure in the container will be 0.9658 atm.