a sample of gaseous substance at 25 degrees Celsius and 0.862atm has a density of 2.6g/l. what is the molecular weight of the substance?
A modified version of the gas law is P*molar mass = density*RT
To find the molecular weight of the substance, we can use the ideal gas law equation:
PV = nRT
where:
P = pressure (0.862 atm)
V = volume (unknown)
n = number of moles (unknown)
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin (25 degrees Celsius = 25 + 273.15 = 298.15 K)
First, let's find the volume. We can rearrange the density equation to find the volume:
density = mass / volume
Therefore,
volume = mass / density
Given that the density is 2.6 g/L, we can calculate the volume:
volume = mass / density = 1 g / (2.6 g/L) = 1 / 2.6 L = 0.385 L
Now we can substitute the values into the ideal gas law equation:
(0.862 atm)(0.385 L) = n(0.0821 L·atm/(mol·K))(298.15 K)
Simplifying the equation:
0.33227 = n(24.41701515)
Dividing both sides by 24.41701515:
n = 0.33227 / 24.41701515 = 0.013 watt
The calculated number of moles (n) is 0.013 mol.
Finally, to find the molecular weight, we divide the mass (in grams) by the number of moles:
molecular weight = mass / n = 1 g / 0.013 mol = 76.92 g/mol
Therefore, the molecular weight of the substance is approximately 76.92 g/mol.
To determine the molecular weight of the gaseous substance, we can use the ideal gas law equation. The ideal gas law equation is:
PV = nRT
Where:
P = pressure in atmospheres (atm)
V = volume in liters (L)
n = number of moles of gas (mol)
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin (K)
We have the following information:
Temperature (T) = 25 degrees Celsius = 25 + 273.15 = 298.15 K
Pressure (P) = 0.862 atm
Density = 2.6 g/L
First, we need to calculate the volume (V) using the given density.
Density = mass / volume
2.6 g/L = mass / V
Since density is mass (g) per unit volume (L), we can rearrange the equation to solve for the volume (V):
V = mass / density
V = mass / 2.6 g/L
Next, we need to calculate the number of moles (n) using the ideal gas law equation:
PV = nRT
Rearranging the equation to solve for the number of moles (n):
n = PV / RT
Substituting the given values:
n = (0.862 atm) * V / (0.0821 L·atm/(mol·K)) * 298.15 K
Now, we can calculate the molecular weight (M) of the substance:
Molecular Weight (M) = mass / number of moles
M = mass / n
Using the given density, we find that the volume (V) is (mass / 2.6 g/L).
Substituting this value into the equation for the number of moles (n), we find:
n = (0.862 atm) * (mass / 2.6 g/L) / (0.0821 L·atm/(mol·K)) * 298.15 K
Finally, substituting the calculated values of the volume (V) and number of moles (n) into the equation for molecular weight (M), we can find the answer.
It is important to note that we would need the mass of the substance to calculate the molecular weight accurately. If the mass is given, you can substitute the given value into the formula.