A gaseous mixture containing carbon monoxide (\text{CO}) and carbon dioxide (\text{CO}_2) … — JAMB UTME

A gaseous mixture containing carbon monoxide ( $\text{CO}$ ) and carbon dioxide ( $\text{CO}_2$ ) has a total mass of $10.0\text{ g}$ . If the mixture contains a total of $2.408 \times 10^{23}$ oxygen atoms, calculate the mass, in grams, of carbon dioxide ( $\text{CO}_2$ ) present in the mixture. $[\text{C} = 12.0, \text{O} = 16.0, N_A = 6.02 \times 10^{23}\text{ mol}^{-1}]$

Answer: 4.4 g

Answer

The mass of carbon dioxide (

\text{CO}_2

) present in the mixture is

4.4\text{ g}

The correct calculation yields 4.4 g by converting the oxygen atom count to 0.40 moles of O atoms, formulating the system of equations for total mass (28x + 44y = 10.0) and total oxygen moles (x + 2y = 0.40), and solving for the mass of CO₂.

Step-by-Step Solution

Determine the molar masses of carbon monoxide and carbon dioxide.

\text{Molar mass of CO} = 12.0 + 16.0 = 28.0\text{ g mol}^{-1}

;

\text{Molar mass of CO}_2 = 12.0 + 2(16.0) = 44.0\text{ g mol}^{-1}

Molar masses are required to relate the mass of each component to its molar quantity.

Calculate the total number of moles of oxygen atoms in the mixture using Avogadro's constant.

n_{\text{O}} = \frac{2.408 \times 10^{23}}{6.02 \times 10^{23}\text{ mol}^{-1}} = 0.40\text{ mol of O atoms}

Avogadro's constant converts particle count to mole quantity.

Set up a system of linear equations representing the total mass and total moles of oxygen atoms.

Let

x = \text{moles of CO}

and

y = \text{moles of CO}_2

.
Equation 1 (Mass):

28x + 44y = 10.0

Equation 2 (Oxygen atoms):

x + 2y = 0.40

CO contains 1 O atom per molecule and CO₂ contains 2 O atoms per molecule.

Solve the system of linear equations for

y

(moles of

\text{CO}_2

From Equation 2,

x = 0.40 - 2y

. Substituting into Equation 1 gives

28(0.40 - 2y) + 44y = 10.0 \implies 11.2 - 56y + 44y = 10.0 \implies 12y = 1.2 \implies y = 0.10\text{ mol}

Algebraic substitution yields the mole quantity of carbon dioxide.

Calculate the mass of

\text{CO}_2

present in the sample.

\text{Mass of CO}_2 = y \times \text{Molar mass} = 0.10\text{ mol} \times 44.0\text{ g mol}^{-1} = 4.4\text{ g}

Multiplying moles of CO₂ by its molar mass gives the required mass in grams.

Key Concept

Mole Concept, Avogadro's Constant, and Gas Mixture Stoichiometry

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