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Chapter 3: Problem 174

When \(\mathrm{M}_{2} \mathrm{~S}_{3}(s)\) is heated in air, it is converted to \(\mathrm{MO}_{2}(s)\). A \(4.000-\mathrm{g}\) sample of \(\mathrm{M}_{2} \mathrm{~S}_{3}(s)\) shows a decrease in mass of \(0.277 \mathrm{~g}\) when it is heated in air. What is the average atomic mass of M?

Short Answer

Expert verified
The average atomic mass of M is approximately 2.87 g/mol.

Step by step solution

01

Write the balanced chemical equation.

First, we need to write the balanced chemical equation for the given reaction: \(M_2S_3(s) + \dfrac{9}{2}O_2(g) → 2MO_2(s) + 3SO_2(g)\)
02

Determine the mass of O2 and S in the sample.

The given mass loss of 0.277 g corresponds to the difference in mass between M2S3 and the products of the reaction. The mass loss is a result of the conversion of sulfur to SO2 and part of the mass of the metal oxide, MO2. Thus, we can calculate the mass of O2 and S in the sample: - Mass of sulfur in M2S3: 4.000 g - 0.277 g = 3.723 g - Mass of oxygen in MO2: 0.277 g - Mass of sulfur (S) = 3.723 g * (3/2) = 5.585 g
03

Determine the molar mass of sulfur and oxygen.

Consult the periodic table to find the molar mass of sulfur (S) and oxygen (O): - Molar mass of sulfur (S): 32.06 g/mol - Molar mass of oxygen (O): 16.00 g/mol
04

Calculate the moles of sulfur and oxygen in the sample.

Now, we can calculate the moles of sulfur and oxygen in the sample using their molar masses: - Moles of S in M2S3: 5.585 g / 32.06 g/mol = 0.174 moles - Moles of O2 in MO2: 0.277 g / 16.00 g/mol = 0.017 moles
05

Use the stoichiometry to find moles of M.

Using the stoichiometry of the balanced chemical equation, we can find the moles of M in the sample: \(Moles\ of\ M = 2 \times Moles\ of\ S = 2 \times 0.174 = 0.348\ moles\)
06

Calculate the average atomic mass of M.

Finally, we can calculate the average atomic mass of M using the mass of M2S3 and the moles of M: \(Average\ atomic\ mass\ of\ M = \dfrac{Mass\ of\ M_{2}S_{3}}{2 \times Moles\ of\ M}\) \(Average\ atomic\ mass\ of\ M = \dfrac{4.000\ g}{2 \times 0.348\ moles }= 2.874\ g/mol\) The average atomic mass of M is approximately 2.87 g/mol.

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Most popular questions from this chapter

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