You are given a 2.9237 g sample of a substance with the generic formula MCl2(H2O)6. After completely drying the sample (which means removing the 6 moles of H2O per mole of MCl2), the sample weighs 1.5941 g. What is the identity of element M? Write your answer as a chemical symbol.

The element represented as M is Co.

Using the formula;

number of moles of hydrated salt = number of moles of anhydrous salt

We obtain;

Mass of hydrated salt/Molar mass of hydrated salt = Mass of anhydrous salt/Molar mass of anhydrous salt

Mass of hydrated salt = 2.9237 g

molar mass of hydrated salt = M + 179

Mass of anhydrous salt =  1.5941 g

Molar mass of anhydrous salt = M + 71

Substituting values;

2.9237/M + 179  =  1.5941/M + 71

2.9237(M + 71) = 1.5941(M + 179)

2.9237M + 207.5827 =  1.5941M + 285.3439

2.9237M -   1.5941M = 285.3439 - 207.5827

1.3296M = 77.7612

M = 77.7612/1.3296

M = 58.5

The element is Co

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M is cobalt (Co)

Explanation:

Step 1: Data given

Mass of MCl2(H2O)6 = 2.9237 grams

After completely drying the sample (which means removing the 6 moles of H2O per mole of MCl2), the sample weighs 1.5941 g.

Step 2: Calculate mass of water

Mass of water = 2.9237 - 1.5941  = 1.3296 grams

Step 3: Calculate moles water

Moles water = mass water / molar mass water

Moles water = 1.3296 grams / 18.02 g/mol

Moles water = 0.07378 moles

Step 4: Calculate moles of the whole substance

For 1 mol MCl2(H2O)6 we have 6 moles H2O

Number of moles of the whole substance = 0.07378 / 6 = 0.01230 moles

Step 5: Calculate molar weight of the substance

Molar weight = mass / moles

Molar weight = 1.5941 grams / 0.01230 moles

Molar weight = 129.6 g/mol

Step 6: Calculate molar weight of M

Molecular weight of M = 129.6 - (2*35.45)

Molecular weight of M = 58.7 g/mol

M is cobalt (Co)