Chemistry solve for x
Chemistry

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Epsom salts, a strong laxative used in veterinary medicine, is a hydrate, which means that a certain number of water molecules are included in the solid structure. The formula for Epsom salts can be written as MgSO_{4} · x H_{2}O, where x indicates the number of moles of H_{2}O per mole of MgSO_{4}. When 5.469 g of this hydrate is heated to 250°C, all the water of hydration is lost, leaving 2.671 g of MgSO_{4}.
WHAT IS THE VALUE OF X? IN THE CORRECT NUMBER OF SIGNIFICANT DIGITS
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DATA:
mass of Epsom salt sample before heating =M_{1}= 5.469g
Mass of Epsom salt sample after heating = M_{2}= 2.671g
Moles of water of hydration=?
SOLUTION:
Mass of water in the washing soda sample= M_{1}M_{2}
= 5.4692.671
Mass of water in the washing soda sample= 2.798g
Moles of water= mass of water in washing soda sample/ molecular mass of water
= 2.798/18
Moles of water = 0.1554mol
Moles of MgSO_{4} after heating = M_{2}/molecular mass of MgSO_{4}
= 2.671/120.32
Moles of MgSO_{4} after heating = 0.0221mol
Since the number of moles of each is not a whole number, we need to find the whole number ratio by dividing each by the smaller of the two:
Moles of MgSO_{4} = 0.0221/0.0221
Moles of MgSO_{4} = 1.00
Moles of water = 0.1554/0.0221
Moles of water= 7.0316
Since the ratio of moles of hydrated washing soda to water of hydration is 1 : 7, the formula would read MgSO_{4} ∙7H_{2}O, and the value of "x" is 7.
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