Question

The density of carbon dioxide is equal to 1.965 kgm⁻³ at 273 K and 1 atm pressure. Calculate the molar mass of CO2.

Answer 1

Final Answer : Molar Mass of CO2 = 44.042g
Assuming gas is Ideal :

Steps and Understanding :
1) Given,
Temperature , T = 273K
Pressure, P = 1atm
Density, d = 1.965 kg/m^3 = 1.965g/L
Gas Constant, R = 0.0821 Latm /K/mole

2)
Let Molar Mass of CO2 be M g.
Then,
Equation :
d = PM/RT
=>
$1 .965 = \frac{1 \times m}{0.0821 \times 273} \\ = > m = 0.0821 \times 273 \times 1.965 \\ = > m = 44.042 \: g \:$

Therefore, Molar Mass of CO2 is 44.042g.

Answer 2

Given conditions ⇒

Density of the Carbon Dioxide = 1.965 kgm⁻³.
Temperature = 273 K.
Pressure = 1 atm.

Now, Using the Formula,
 Pa/RT = Density
where, as is the molar mass of the gas
R is the gas constant equals to the 0.0821 liter-atm K⁻¹ mol⁻¹.

∴ 1 × a/(0.0821 × 273) = 1.965
∴ a = 1.965 × 0.0821 × 273
⇒ a = 44.04 ≈ 44 g/mol.


Hence, the molar mass of the Carbon Dioxide is approximately 44 g/mole. 



Hope it helps.