This same substance is a gas with a density of 1.25 g/L at 127o
C and a pressure of 400
torr. What is its molar mass ?
P*molar mass = density*RT
P must be in atm. 760 torr = 1 atm.
To find the molar mass of a gas, we can use the Ideal Gas Law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = number of moles
R = Ideal Gas Constant
T = Temperature in Kelvin
First, we need to convert the given temperature from Celsius to Kelvin. The conversion formula is:
K = °C + 273.15
So, 127°C in Kelvin is:
T = 127 + 273.15 = 400.15 K
Next, we can rearrange the Ideal Gas Law equation to solve for the number of moles (n):
n = (PV) / (RT)
Substituting the given values:
P = 400 torr = 400/760 atm (since 1 atm = 760 torr)
V = 1.25 L
R = 0.0821 L·atm/(mol·K)
n = ((400/760) x 1.25) / (0.0821 x 400.15)
n ≈ 0.0822 moles
The molar mass (M) can then be calculated using the formula:
M = molar mass / number of moles
Rearranging the formula:
molar mass = M x number of moles
Substituting known values:
M = (1.25 g/L) / 0.0822 mol
M ≈ 15.20 g/mol
Therefore, the molar mass of the substance is approximately 15.20 g/mol.
To find the molar mass of a gas, you can use the ideal gas law equation, which is:
PV = nRT
Where:
P is the pressure of the gas (in torr),
V is the volume of the gas (in liters),
n is the number of moles of the gas,
R is the ideal gas constant (0.08206 L·atm/mol·K),
and T is the temperature of the gas (in Kelvin).
First, we need to convert the given temperature from degrees Celsius to Kelvin. To do this, we use the formula:
T (K) = T (°C) + 273.15
So, the temperature in Kelvin would be:
T = 127 + 273.15 = 400.15 K
Next, we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = (PV) / (RT)
Now, let's plug in the given values:
P = 400 torr
V = 1.25 L
R = 0.08206 L·atm/mol·K
T = 400.15 K
Substituting these values into the equation, we get:
n = (400 torr * 1.25 L) / (0.08206 L·atm/mol·K * 400.15 K)
Simplifying the equation, we find:
n ≈ 19.11 mol
Now that we have the number of moles (n), we can calculate the molar mass (M) using the formula:
M (g/mol) = m (g) / n (mol)
However, we are given the density of the gas (d) instead of the mass. Density is defined as mass per unit volume:
d = m (g) / V (L)
Rearranging this equation to solve for mass (m), we get:
m (g) = d (g/L) * V (L)
Now, substituting the given values:
d = 1.25 g/L
V = 1.25 L
m (g) = 1.25 g/L * 1.25 L = 1.5625 g
Finally, we can calculate the molar mass (M):
M (g/mol) = m (g) / n (mol)
M ≈ 1.5625 g / 19.11 mol
So, the molar mass of the gas is approximately 0.082 g/mol.