If 0.896g of a gas occupies a 250mL flask at 20 degree celcius and 760 mmHg of pressure, what is the molar mass of the gas?
Note the correct spelling of celsius.
Use PV = nRT and solve for n, then
n = grams/molar mass.
To find the molar mass of the gas, 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 given volume from milliliters to liters:
250 mL = 250/1000 = 0.250 liters
Next, let's convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 20 + 273.15 = 293.15 K
Plugging in the values into the ideal gas law equation:
PV = nRT
(760 mmHg) * (0.250 L) = n * (0.0821 L·atm / mol·K) * (293.15 K)
To get the pressure in atm, we need to convert mmHg to atm:
1 atm = 760 mmHg
So, the pressure becomes:
(760 mmHg) * (1 atm / 760 mmHg) = 1 atm
Now we can rewrite the equation as:
(1 atm) * (0.250 L) = n * (0.0821 L·atm / mol·K) * (293.15 K)
Simplifying:
n = (1 atm * 0.250 L) / (0.0821 L·atm / mol·K * 293.15 K)
Calculating:
n = 0.010055 mol
Finally, we can find the molar mass (M) using the formula:
molar mass (M) = mass / number of moles
Given that the mass of the gas is 0.896g and the number of moles is 0.010055 mol, we can substitute these values into the formula:
M = 0.896g / 0.010055 mol
Calculating:
M ≈ 89.14 g/mol
Therefore, the molar mass of the gas is approximately 89.14 g/mol.