Complete the statement by calculating the required volume of gas at STP and the mass of me… — JAMB UTME

Complete the statement by calculating the required volume of gas at STP and the mass of metal produced in the following reduction reaction.

Answer:When

16.0\text{ g}

of iron(III) oxide (

Fe_2O_3

) is completely reduced by carbon monoxide gas according to the equation:

Fe_2O_3(s) + 3CO(g) \rightarrow 2Fe(s) + 3CO_2(g)

the volume of carbon monoxide gas consumed at STP is 【6.72 dm3】, and the mass of iron metal produced is 【11.2 g】.

[Relative atomic masses:

\text{Fe} = 56

\text{O} = 16

; Molar volume of gas at STP

= 22.4\text{ dm}^3\text{ mol}^{-1}

]

Answer

The volume of carbon monoxide consumed at STP is

6.72\text{ dm}^3

and the mass of iron metal produced is

11.2\text{ g}

Based on the stoichiometry of the reaction

Fe_2O_3(s) + 3CO(g) \rightarrow 2Fe(s) + 3CO_2(g)

1\text{ mol}

(

160\text{ g}

) of

Fe_2O_3

reacts with

3\text{ mol}

(

0.30\text{ mol}

for

16.0\text{ g}

) of

CO

gas, yielding a volume of

6.72\text{ dm}^3

at STP, and produces

2\text{ mol}

(

0.20\text{ mol}

for

16.0\text{ g}

) of

Fe

, corresponding to

11.2\text{ g}

Step-by-Step Solution

Calculate the molar mass of

Fe_2O_3

and determine the number of moles of

Fe_2O_3

present.

Molar mass of

Fe_2O_3 = (2 \times 56) + (3 \times 16) = 160\text{ g mol}^{-1}

. Moles of

Fe_2O_3 = \frac{16.0\text{ g}}{160\text{ g mol}^{-1}} = 0.10\text{ mol}

Converting given mass to moles is required for stoichiometric mole-ratio calculations.

Use the mole ratio from the balanced equation to find the moles and volume of

CO(g)

required at STP.

From the balanced equation,

1\text{ mol } Fe_2O_3

reacts with

3\text{ mol } CO

.
Moles of

CO = 3 \times 0.10\text{ mol} = 0.30\text{ mol}

.
Volume of

CO

at STP

= 0.30\text{ mol} \times 22.4\text{ dm}^3\text{ mol}^{-1} = 6.72\text{ dm}^3

Gas volume at STP is obtained by multiplying moles of gas by the molar volume (

22.4\text{ dm}^3\text{ mol}^{-1}

Use the mole ratio from the balanced equation to calculate the mass of iron (

Fe

) produced.

From the equation,

1\text{ mol } Fe_2O_3

produces

2\text{ mol } Fe

.
Moles of

Fe = 2 \times 0.10\text{ mol} = 0.20\text{ mol}

.
Mass of

Fe = 0.20\text{ mol} \times 56\text{ g mol}^{-1} = 11.2\text{ g}

Mass of product is calculated by multiplying its moles by its relative atomic mass.

Key Concept

Mass-Mass and Mass-Volume Stoichiometric Calculations

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