1.45 g of an unknown gas at 53 °C and 1.10 atm is stored in a 1.85-L flask.
What is the density of the gas
what is the molar mass of the gas
The problem doesn't say the conditions you want for the density; i.e., is that density at 53 C and 1.10 atm or density at STP. I will assume you want it at STP. Therefore, we must correct the volume from 1.85 L to the volume at STP. So T goes from 326 K (273 + 53) to 273 K and pressure goes from 1.10 atm to 1.00 atm.
1.85 L x (273/326) x (1.10/1.00) = about 1.70 L but you should go through that yourself.
Then density = 1.45 g/1.70 = ?
Then density of a gas at STP = molar mass/22.4 L. You know density at STP, solve for molar mass.
To find the density of the gas, you need to use the ideal gas law equation, which is:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
First, let's convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 53 + 273.15 = 326.15 K
Next, rearrange the ideal gas law equation to solve for density (d):
d = (PM) / (RT)
Where:
d = density
P = pressure (in atm)
M = molar mass (in grams/mole)
R = gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
Now, plug in the values given in the problem:
P = 1.10 atm
V = 1.85 L
T = 326.15 K
Substitute these values into the equation:
d = (1.10 atm * M) / (0.0821 L·atm/(mol·K) * 326.15 K)
Simplify the equation:
d = (1.10 atm * M) / (26.854 L·atm/(mol·K))
Finally, simplify further:
d = 0.041039 M/atm
So, the density of the gas is 0.041039 grams per liter per atm.
To find the molar mass of the gas, you'll need to know the density. However, you can use the density to determine the molar mass.
Rearranging the equation for density:
d = (PM) / (RT)
Solve for M:
M = (dRT) / P
Plug in the values given in the problem:
d = 0.041039 g/L/atm (density found earlier)
R = 0.0821 L·atm/mol·K (gas constant)
T = 326.15 K (temperature in Kelvin)
P = 1.10 atm (pressure)
Substitute these values into the equation:
M = (0.041039 g/L/atm * 0.0821 L·atm/(mol·K) * 326.15 K) / 1.10 atm
Simplify the equation:
M = 10.8 g/mol
Therefore, the molar mass of the gas is 10.8 grams per mole.