What is the density (in grams per liter) of a gas at STP if 4.16 L of the gas in a bulb at 43.7 °C, and 737.9 mm Hg weighs 0.262 g?
The general gas formula can be modified from PV = nRT to
P*molar mass = density*RT
Substitute and solve for density.
To find the density (in grams per liter) of a gas at STP (Standard Temperature and Pressure), you will need to use the ideal gas law equation, which is:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of the gas
R = ideal gas constant
T = temperature of the gas in Kelvin
First, we need to convert the given values to the appropriate units:
- The volume is given as 4.16 L.
- The temperature is given as 43.7 °C.
- The pressure is given as 737.9 mm Hg.
- The mass of the gas is given as 0.262 g.
Let's start by converting the temperature from Celsius to Kelvin:
To convert Celsius to Kelvin, you need to add 273.15. So, 43.7 °C + 273.15 = 316.85 K.
Next, we need to convert the pressure from mm Hg to atm because the ideal gas constant is commonly expressed in atm:
1 atm = 760 mm Hg
So, 737.9 mm Hg / 760 = 0.9714 atm.
Now, we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Substituting the given values, we get:
n = (0.9714 atm) x (4.16 L) / [(0.0821 L·atm/(mol·K)) x (316.85 K)]
Now, we can calculate the number of moles (n).
n = 0.0427 mol
Finally, we can find the density by dividing the mass of the gas by the volume:
Density = Mass / Volume
Density = 0.262 g / 4.16 L
Now, you can calculate the density of the gas at STP by dividing the mass by the volume.