Chemistry - Mole Concept Question with Solution | TestHub

Question Explanation: Find the mass fraction of the metal in the second oxide ${\mathrm{M}}_2{\mathrm{O}}_3$.

Concept: This question is based on mass fraction.

Solution: The mass fraction of oxygen in MO is 0.225. This means that for every 1 gram of the oxide, 0.225 grams is oxygen.

The formula for the mass fraction of oxygen is:

$$MassfractionofO=\frac{AtomicmassofO}{MolarmassofMO}$$

Let $A_M$ be the atomic mass of metal M and 16 be the atomic mass of oxygen.

$$0.225=\frac{16}{A_M+16}$$

Now, solve for $A_M$:

$$0.225(A_M+16)=16$$

$$0.225A_M+3.6=16$$

$$0.225A_M=12.4$$

$$A_M=\frac{12.4}{0.225}\approx 55.11$$

The question asks for the mass fraction of the metal in the second oxide (M₂O₃). Note that while the problem mentions the mass fraction of oxygen in the second oxide is 0.304, we can calculate the mass fraction directly or simply use the complementary value.

The total mass fraction of any compound is 1. Therefore:

$$MassfractionofMetal=1-Massfractionofoxygen$$

$$MassfractionofMetal=1-0.304$$

$$MassfractionofMetal=0.696$$

Verification using Atomic Mass:

We can double-check this using the atomic mass $A_M\approx 55.11$ we found:

$$MassfractionofM=\frac{2\times A_M}{(2\times A_M)+(3\times 16)}$$

$$MassfractionofM=\frac{2\times 55.11}{(2\times 55.11)+(3\times 16)}=\frac{110.22}{110.22+48}=\frac{110.22}{158.22}\approx 0.6966$$

The result confirms that the mass fraction is approximately 0.696.

Final Answer: Option (A)