If 0.385 g of gas occupies a volume of 200 mL at -73 oC and 750 torr, what is the molecular mass of the gas?
a) 21.4
b) 32.0
c) 44.0
d) 48.0
Someone can help me this answer please..?
PV = nRT
Calculate n = number of moles.
Then n = grams/molar mass.
Calculate molar mass.
To find the molecular mass of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, let's convert the given values to the appropriate units:
- The temperature -73 oC needs to be converted to Kelvin. The Kelvin temperature scale is obtained by adding 273.15 to the Celsius temperature, so -73 oC + 273.15 = 200.15 K.
- The volume 200 mL needs to be converted to liters. There are 1000 mL in a liter, so 200 mL / 1000 mL/L = 0.2 L.
- The pressure 750 torr needs to be converted to atm. There are 1 atm in 760 torr, so 750 torr / 760 torr/atm = 0.9868 atm.
Now we can substitute the values into the ideal gas law equation:
(0.9868 atm)(0.2 L) = (n)(0.0821 L·atm/(mol·K))(200.15 K)
Simplifying the equation:
0.19736 = (n)(0.0821)(200.15)
0.19736 = 16.862715n
Solving for moles (n):
n = 0.19736 / 16.862715
n ≈ 0.01168 moles
Next, we can calculate the molecular mass using the formula:
molecular mass = mass / moles
Given that the mass is 0.385 g, we can substitute these values:
molecular mass = 0.385 g / 0.01168 moles
Simplifying the equation:
molecular mass ≈ 32.999
So, the molecular mass of the gas is approximately 32.999 g/mol.
Comparing this value to the answer choices, we can see that the closest option is b) 32.0. Therefore, the correct answer is b) 32.0.