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A container holds 15.0 g of phosphorous gas at a pressure of 2.0 atm and a temperature of 20.0 Celsius. What is the density of the gas?

2.57 g/L
12.3 g/L
180 g/L
0.40 g/L

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MissPhiladelphia
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. We calculate as follows:

PV = nRT
PV = mRT/ Molar mass
m/V = P(molar mass)/RT
Density = P(molar mass)/RT 
Density = 2.0 ( 30.97 ) / 0.08206 ( 20 + 273.15) = 2.57 g/L <----First option

Answer: Density of the gas is 2.57 g/L.

Explanation: Converting the mass of phosphorous gas into its moles using the formula:

[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex]

Given mass of phosphorous gas = 15 g

Molar mass of phosphorous gas = 31 g/mol

Using above equation, we get

[tex]n=\frac{15g}{31g/mol}=0.484moles[/tex]

Using Ideal gas equation, which is:

[tex]PV=nRT[/tex]

Given:

P = 2 atm

[tex]T=20^oC=(273+20)K=293K[/tex]    (Conversion Factor: [tex]0^oC=273K[/tex] )

n = 0.484 moles (Calculated above)

[tex]R=0.082057\text{ L atm }mol^{-1}K^{-1}[/tex]  (Gas Constant)

Putting all the values in above equation, we calculate the number of moles.

[tex]2atm\times V=(0.484moles)(0.082057\text{ L atm }mol^{-1}K^{-1})(293K)[/tex]

V = 5.818 L

Now, to calculate density, we use the formula:

[tex]Density=\frac{Mass}{Volume}[/tex]

[tex]Density=\frac{15g}{5.818L}[/tex]

Density = 2.57 g/L