32g of hydrated magnesium sulphate $M g S O_{4} . x H_{2} O$ is dissolved in 84g of water. The solution freezes at $- {4.836}^{0} C$ . If $K_{f} =$ 1.86 K kg $m o l^{- 1}$ and $M g S O_{4}$ is a strong electrolyte, then the value of $x$ is:

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Solution

Molar mass of salt $= 120 + 18 x$
Mass of water present in the salt $= \frac{18 x}{120 + 18 x} \times 32 g$
Molality of the solution $= \frac{32}{120 + 18 x} \times ⎡ ⎢ ⎢ ⎢ ⎣ \frac{1000}{84 + \frac{18 \times 32 x}{120 + 18 x}} ⎤ ⎥ ⎥ ⎥ ⎦ = \frac{4000}{1260 + 261 x}$
$Δ T_{f} = 4.836 = 2 \times 1.86 \times \frac{4000}{1260 + 261 x}$
$x = 6.9 \approx 7$

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32g of hydrated magnesium sulphate MgSO4.xH2O is dissolved in 84g of water. The solution freezes at −4.8360C. If Kf=1.86 K kg mol−1 and MgSO4 is a strong electrolyte, then the value of x is:

Molar mass of salt =120+18xMass of water present in the salt =18x120+18x×32gMolality of the solution =32120+18x×⎡⎢ ⎢ ⎢⎣100084+18×32x120+18x⎤⎥ ⎥ ⎥⎦=40001260+261xΔTf=4.836=2×1.86×40001260+261xx=6.9≈7

32g of hydrated magnesium sulphate $M g S O_{4} . x H_{2} O$ is dissolved in 84g of water. The solution freezes at $- {4.836}^{0} C$ . If $K_{f} =$ 1.86 K kg $m o l^{- 1}$ and $M g S O_{4}$ is a strong electrolyte, then the value of $x$ is: