Determining the Relative Atomic Mass of Metal M in Hydride MH?

Introduction

The problem presented here involves determining the relative atomic mass of a metal M in the hydride MH?, where MH? contains 90% of its mass in metal M. The solution to this problem involves basic principles of stoichiometry and molar mass calculations. Let's break down the solution step-by-step.

Solution

To solve this problem, we start by assuming the relative atomic mass of metal M is x amu (Atomic Mass Units).

Step 1: Calculate the Molecular Mass of MH?

From the given information:

M has a mass of x amu. Hydrogen (H) has a molar mass of 1 g/mol, and there are 3 hydrogen atoms, contributing 3 g/mol to the molecular mass.

Hence, the molecular mass of MH? can be calculated as x 3 amu.

Step 2: Use the Given Mass Composition

Given that 90% of the mass of MH? is due to metal M, we can set up the following equation:

Molar Mass of MH? × 0.90 Mass of M

This translates to:

(x 3) × 0.90 x

Step 3: Solve the Equation

Rearranging the equation:

0.9 2.70 x

0.9 - x -2.70

-0.1 -2.70

x 27 amu

Hence, the relative atomic mass of metal M is 27 amu.

Alternative Approaches

Let's explore the alternative approaches to verify the solution:

Approach 1: Calculation Using Given Data

Given:

- 100 g of MH? contains 90 g of metal M and 10 g of hydrogen (H).

Since the molar mass of hydrogen is 1 g/mol, 10 g of hydrogen is 10 moles of hydrogen.

The number of moles of M is one-third that of hydrogen, so M has 3.33 moles.

Therefore, 90 g of M is 3.33 moles of M, giving a molar mass of 27 g/mol for metal M.

Hence, the metal M is aluminum (Al).

Approach 2: Simplified Calculation

Since 10 g of hydrogen corresponds to 10 moles, we can use the following simplified calculation:

Let's denote the molar mass of MH? as M? 3. Since 10 g (10 moles) of H corresponds to 90 g of MH? (which is 90% of MH?), we can find the molar mass of MH? as follows:

10 g of H 10 moles

Hence, 90 g of M is 1/3 of 27 amu, giving a molar mass of 27 amu for metal M.

The metal is again aluminum (Al).

Conclusion

By following the steps outlined in the solution, we can determine that the relative atomic mass of metal M in the hydride MH? is 27 amu. This aligns with the properties of aluminum, and the additional calculations provide further validation.

References

1. Chemical Calculator for MH? Molecular Weight

2. Boundless Chemistry