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Difficulty: MediumRelative Atomic Mass, Relative Molecular Mass, and Carbon-12 Scale

A sample of hydrated magnesium tetraoxosulfate(VI) has the formula MgSO4⋅xH2OMgSO_4 \cdot xH_2O. If the relative molecular mass of the hydrated salt is 246246, what is the value of xx? [Mg=24,S=32,O=16,H=1][Mg = 24, S = 32, O = 16, H = 1]

  1. A
    55
  2. B
    66
  3. 77Answer
  4. D
    1010

Answer

The value of xx is 77.
The relative formula mass of anhydrous MgSO4MgSO_4 is calculated as 24+32+(4×16)=12024 + 32 + (4 \times 16) = 120. Subtracting this from the total relative molecular mass of 246246 leaves 126126 for the water of crystallization (xH2OxH_2O). Since each H2OH_2O molecule has a relative mass of (2×1)+16=18(2 \times 1) + 16 = 18, dividing 126126 by 1818 gives x=7x = 7.

Step-by-Step Solution

1
Calculate the relative formula mass of the anhydrous salt MgSO4MgSO_4.
24+32+(4×16)=12024 + 32 + (4 \times 16) = 120
Summing the relative atomic masses of magnesium, sulfur, and four oxygen atoms gives the mass of the anhydrous portion.
2
Calculate the relative molecular mass of a single water molecule H2OH_2O.
(2×1)+16=18(2 \times 1) + 16 = 18
Two hydrogen atoms and one oxygen atom combine to give a relative molecular mass of 18.
3
Set up the equation for the relative molecular mass of the hydrated salt and solve for xx.
120+18x=246  ⟹  18x=126  ⟹  x=7120 + 18x = 246 \implies 18x = 126 \implies x = 7
Subtracting the anhydrous mass of 120 from the total mass of 246 gives 126 for the water content, and dividing by 18 yields 7 molecules of water of crystallization.

Key Concept

Relative Molecular Mass of Hydrated Salts
Estimated Time:1m 30s
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Topics

Relative Atomic Mass, Relative Molecular Mass, and Carbon-12 Scale

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