Calculating Nitrogen Gas Density at 20°C: Solutions and Explanation

[bballboy1191]

Homework Statement

What is the density of nitrogen gas at a temperature of 20 degrees celcius

Homework Equations

p= m/v??
Pv=nRT??
change in volume = (volumetric coefficicient of thermal expansion)(initial volume)(change in temperature)??

The Attempt at a Solution

i tried to use the coefficient of thermal expansion to find the changing volume but gasses don't have values for thermal expansion.

now I am not sure what to do
any help is appreciated

 

[Delphi51]

I remember that an ideal gas at standard pressure and temperature has one mole of molecules in a volume of 22.4 Liters. If you know the molar mass for nitrogen, you should be able to get the density from this. What is "standard" temperature in your class?

 

[nlightner]

The density of nitrogen gas at 20°C can be calculated using the ideal gas law, which is represented by the equation PV = nRT. In this equation, P represents the pressure of the gas, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. Since the temperature is given in Celsius, it must be converted to Kelvin by adding 273.15.

To solve for density, we can rearrange the equation to get P = (nRT)/V. The number of moles (n) can be calculated by dividing the mass of the gas by its molar mass. The molar mass of nitrogen gas is approximately 28 grams per mole.

Once we have the value for pressure, we can use the ideal gas law again to calculate the volume of the gas. Rearranging the equation, we get V = (nRT)/P. We can then use the volume and the mass of the gas to calculate its density using the formula D = m/V, where D is density, m is mass, and V is volume.

Alternatively, we can use the relationship between pressure, volume, and temperature for an ideal gas, which is PV = NkT, where N is the number of particles, k is the Boltzmann constant, and T is the temperature in Kelvin. By rearranging the equation to get N = (PV)/(kT), we can then use Avogadro's number (6.022 x 10^23) to calculate the number of moles, which can then be used to find the density as mentioned above.

In summary, the density of nitrogen gas at 20°C can be calculated using the ideal gas law and the relationship between pressure, volume, and temperature for an ideal gas. It is important to remember to convert all temperature values to Kelvin when using these equations.