Respuesta :
Density is a value for mass, such as kg, divided by a value for volume, such as m3. Density is a physical property of a substance that represents the mass of that substance per unit volume. For gases we use the ideal gas equation to solve for density. We do as follows:
PV = nRT
PV = mRT / MM
Density = m/V = PMM / RT
From the given conditions of the nitrogen gas, we substitute the given values as follows:
Density = PMM / RT
Density = 1.5 atm ( 28.02 g / mol) / (0.08205 L-atm / mol-K) (290 K)
Density = 1.77 g/L
Therefore, the density of the gas is 1.77 g per liter.
Explanation:
The given data is as follows.
n = 0.020 moles, P = 1.5 atm
T = 290 K, molar mass of nitrogen = 14.0 g/mol
R = 8.314 J/mol, d = ?
It is known that the relation between density, pressure, and temperature is as follows.
P = [tex]\frac{d}{\text{molar mass}} \times RT[/tex]
Putting the given values into the above relation and calculate the density as follows.
P = [tex]\frac{d}{\text{molar mass}} \times RT[/tex]
1.5 atm = [tex]\frac{d}{14.0 g/mol} \times 8.314 \times 290 K[/tex]
d = [tex]\frac{1.5 atm \times 14.0 g/mol}{8.314 L atm/mol K \times 290 K}[/tex]
= [tex]1.74 \times 10^{-4}[/tex] g
Thus, we can conclude that density of the given gas is [tex]1.74 \times 10^{-4}[/tex] g.
