High School

(a) In a 20.0 L steel container, we have 77.7 g of CO2(g), 99.9 g of N2(g), and 88.8 g of an unknown gas. The temperature is 25.0°C, and the total pressure is 9.99 atm.

What is the molar mass of the unknown gas?

The molar masses of C, N, and O are 12.01, 14.01, and 16.00 g/mol, respectively.

Answer :

The molar mass of the unknown gas in the steel container is 31.3637 g/mol.

Given that:

Pressure, P = 9.99 atm

The volume of the container, V = 20 L

R = 0.0821 atm L / mol.K

Temperature, T = 25°C

= 25 + 273.16

= 298.16 K

Number of moles, n = n(C0₂) + n(N₂) + n(unknown gas)

Now, molar mass = Mass / Number of moles.

The molar mass of CO₂ = 12.01 + 2(16) = 44.01 g/mol

So, n(C0₂) = 77.7 / 44.01 = 1.7655

The molar mass of N₂ = 2 (14.01) = 28.02 g/mol

So, n(N₂) = 99.9 / 28.02 = 3.5653

So, n = 1.7655 + 3.5653 + n(x), where x represents the unknown gas.

Substitute the values in the gas equation.

PV = n RT

9.99 × 20 = (1.7655 + 3.5653 + n(x)) × 0.0821 × 298.16

199.8 = 24.478936(5.3308 + n(x))

5.3308 + n(x) = 8.162

n(x) = 2.8313 moles

So, the molar mass of the unknown gas is:

m = 88.8 / 2.8313

= 31.3637 g/mol

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