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Chapter 3: Problem 100

A 0.622 g sample of a metal oxide with the formula \(\mathrm{M}_{2} \mathrm{O}_{3}\) is converted to \(0.685 \mathrm{g}\) of the sulfide, MS. What is the atomic mass of the metal M?

Short Answer

Expert verified
To get the short answer, solve the final equation obtained in Step 3. That will give the atomic mass of the metal M in grams per mole.

Step by step solution

01

Derive the expression for mass in metal oxide

The formula for metal oxide is provided as M2O3. This means that in one mole of metal oxide, there are 2 moles of the metal M. Given that the molar mass is equal to grams per mole, the atomic mass of M in the metal oxide can be represented as follows: \(2M_{mass} + 3(16) = 0.622g\) (where 16 is the atomic mass of oxygen).
02

Derive the expression for mass in metal sulfide

The formula for metal sulfide is MS, meaning that in one mole of metal sulfide, there's one mole of the metal M. The atomic mass of M in the metal sulfide can therefore be represented as follows: \(M_{mass} + 32.07 = 0.685g\) (where 32.07 is the atomic mass of sulfur).
03

Solve the system of equations

Now, there are two equations with M_mass as the variable. This system of equations can be solved by substitution or elimination method. Let’s choose substitution in this case, isolate M_mass in the second equation and substitute it into the first equation to find the atomic mass of M.

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