Calculate the Molecular Weight (MW) of a hydrocarbon as if 0.5813 g of this gas completely fills a 250.0 mL flask at a temperature of 24.4 C and pressure of 742.6 mmHg. Show all work and assume ideal behavior.
Use PV = nRT, solve for n, then n = grams/molar mass. Solve for molar mass(molecular weight).
Remember P must be in atmospheres, V in liters, and T in kelvin.
what does the R stand for again? the grams?
In the units I quoted R =- 0.08206 L*atm/mol*K.
To calculate the molecular weight (MW) of a hydrocarbon using the given information, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure in atm
V = volume in liters
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin
First, we need to convert the given values to the appropriate units:
Pressure:
Convert 742.6 mmHg to atm by dividing it by 760 mmHg in 1 atm:
Pressure = 742.6 mmHg / 760 mmHg/atm = 0.975 atm
Volume:
Convert 250.0 mL to liters by dividing it by 1000 mL/L:
Volume = 250.0 mL / 1000 mL/L = 0.250 L
Temperature:
Convert 24.4°C to Kelvin by adding 273.15:
Temperature = 24.4 + 273.15 = 297.55 K
Now, we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Plugging in the values:
n = (0.975 atm) (0.250 L) / (0.0821 L·atm/mol·K) (297.55 K)
Calculate the value using a calculator:
n ≈ 0.0102 moles
Next, to calculate the molecular weight (MW), we need to find the molar mass of the hydrocarbon. Since we don't have the specific formula, let's assume the hydrocarbon is an alkane.
The general formula for an alkane is CnH(2n+2). To find the value of n, we can consider the molar mass of the hydrocarbon.
Given that 0.5813 g of the gas completely fills the flask, we can assume that the molar mass is equal to the molecular weight (in grams).
MW = m/n
Plugging in the values:
MW = 0.5813 g / 0.0102 moles
Calculate the value using a calculator:
MW ≈ 56.908 g/mol
Therefore, the molecular weight (MW) of the hydrocarbon is approximately 56.908 g/mol.