To determine the relative atomic mass of metal M, we need to consider the percentage composition of the hydride MH3.
Given that MH3 contains 90% of M by mass, we can infer that the remaining 10% is contributed by the hydrogen atoms in the compound. Since there are three hydrogen atoms in MH3, their combined mass represents 10% of the total compound mass.
Let's assume the molar mass of MH3 is M_MH3 g/mol, and the molar mass of M is M_M g/mol.
The mass of M in MH3 is 90% of the total mass of MH3, which can be expressed as:
0.9 * M_MH3 = M_M
Since MH3 contains one M atom and three H atoms, its molar mass can be calculated as:
M_MH3 = M_M + (3 * M_H)
Now we can rearrange the equation to solve for M_M:
0.9 * (M_M + (3 * M_H)) = M_M
0.9 * M_M + 2.7 * M_H = M_M
0.9 * M_M - M_M = -2.7 * M_H
-0.1 * M_M = -2.7 * M_H
M_M = (2.7 * M_H) / 0.1
Therefore, the relative atomic mass of metal M can be calculated using the ratio of the molar masses:
Relative atomic mass of M = M_M / M_U
where M_U is the unified atomic mass unit (approximately 1 g/mol).
Please note that to obtain a numerical value for the relative atomic mass of M, the molar mass of hydrogen (M_H) would need to be provided or assumed.