A 0.109g sample of a pure gaseous compound occupies 112ml at 100degrees and 750torr: what is the molecular weight of the compound. ANS=(30.2g,mol). Please I need the solution
30.2 g/mL
To find the molecular weight of the compound, we need to use the ideal gas law equation. The ideal gas law equation is given as:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
Given:
Mass of compound = 0.109 g
Volume of compound = 112 mL = 0.112 L
Pressure = 750 torr
Temperature = 100 degrees C = 100 + 273.15 = 373.15 K (temperature must be in Kelvin)
First, let's calculate the number of moles of the compound using the ideal gas law equation. Rearranging the equation to solve for n, we have:
n = PV / RT
Now, we can substitute the given values into the equation:
n = (750 torr * 0.112 L) / (0.0821 L atm/mol K * 373.15 K)
Next, we convert torr to atm:
1 torr = 1/760 atm
n = (750/760 * 0.112) / (0.0821 * 373.15)
After performing the calculation, we find:
n ≈ 0.00374 moles
Finally, we can calculate the molecular weight (M) using the formula:
Molecular weight (M) = Mass (m) / Moles (n)
M = 0.109 g / 0.00374 moles
After performing this calculation, we find:
M ≈ 29.09 g/mol
Therefore, the molecular weight of the compound is approximately 29.09 g/mol.
To find the molecular weight of the compound, you can use the ideal gas 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, let's convert the given values to the appropriate units:
- The mass of the sample is given as 0.109g.
- The volume is given as 112ml, which should be converted to liters. 1 mL is equivalent to 0.001 L, so 112 ml = 112 x 0.001 L = 0.112 L.
- The temperature is given as 100 degrees, which should be converted to Kelvin. To convert Celsius to Kelvin, add 273.15. So, 100 degrees Celsius = 100 + 273.15 Kelvin = 373.15 K.
- The pressure is given as 750 Torr, but the ideal gas equation requires pressure in atm. 1 atm is equivalent to 760 Torr, so 750 Torr = 750/760 atm = 0.9868 atm.
Now, plug these values into the ideal gas equation:
(0.9868 atm) * (0.112 L) = n * (0.0821 L·atm/mol·K) * (373.15 K)
Simplifying the equation:
0.1103 = n * 30.65
Solving for n, the number of moles:
n = 0.1103 / 30.65
n ≈ 0.0035987 mol
Finally, to find the molecular weight, divide the mass of the sample (0.109g) by the number of moles (0.0035987 mol):
Molecular weight = 0.109g / 0.0035987 mol
Molecular weight ≈ 30.334 g/mol
So, the molecular weight of the compound is approximately 30.3 g/mol.
We try not to do your work for you. Use PV = nRT and solve for n = number of mols.
Then n = grams/molar mass. You know grams and n, solve for molar mass.