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Chapter 3: Problem 54

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 \(\mathrm{MgSO}_{4} \cdot x \mathrm{H}_{2} \mathrm{O}\), where \(x\) indicates the number of moles of \(\mathrm{H}_{2} \mathrm{O}\) per mole of \(\mathrm{MgSO}_{4}\). When \(5.061 \mathrm{~g}\) of this hydrate is heated to \(250{ }^{\circ} \mathrm{C}\), all the water of hydration is lost, leaving \(2.472 \mathrm{~g}\) of \(\mathrm{MgSO}_{4}\). What is the value of \(x\) ?

Short Answer

Expert verified
The value of \(x\) in the formula for Epsom salts, \(MgSO_{4} \cdot xH_{2}O\), is 7. Consequently, the formula for Epsom salts is \(MgSO_{4} \cdot 7H_{2}O\).

Step by step solution

01

Calculate moles of MgSO4

To find the moles of MgSO4, we will first find the molar mass of MgSO4 and then use the formula: Moles = Mass / Molar Mass. Molar mass of MgSO4 can be calculated using the formula: \(Molar \, Mass = Mass_{Mg} + Mass_{S} + 4 \times Mass_{O} = 24.305 \mathrm{~g/mol} + 32.07 \mathrm{~g/mol} + 4 \times 16.00 \mathrm{~g/mol} = 120.37 \mathrm{~g/mol}\) Next, we will find the moles of MgSO4 using the formula: \(Moles = \frac{Mass}{Molar \, Mass} = \frac{2.472 \mathrm{~g}}{120.37 \mathrm{~g/mol}} = 0.02053 \mathrm{~mol}\)
02

Calculate moles of water

To find the moles of water, we will first find the mass of the water lost during the dehydration process. Then we will find the moles of water using the formula: Moles = Mass / Molar Mass. Mass of water lost = Mass of hydrate - Mass of anhydrous salt \(Mass \, of \, water \, lost = 5.061 \mathrm{~g} - 2.472 \mathrm{~g} = 2.589 \mathrm{~g}\) Now we will find the moles of water using the formula: \(Moles = \frac{Mass}{Molar \, Mass} = \frac{2.589 \mathrm{~g}}{18.015 \mathrm{~g/mol}} = 0.1437 \mathrm{~mol}\)
03

Calculate the value of x

With the moles of MgSO4 and water calculated, we can find the value of x using the formula: \(x = \frac{Moles \, of \, H_{2}O}{Moles \, of \, MgSO_{4}}\) \(x = \frac{0.1437 \mathrm{~mol}}{0.02053 \mathrm{~mol}} = 7.00\) Therefore, the formula for Epsom salts is: \(MgSO_{4} \cdot 7H_{2}O\).

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Most popular questions from this chapter

A chemical plant uses electrical energy to decompose aqueous solutions of \(\mathrm{NaCl}\) to give \(\mathrm{Cl}_{2}, \mathrm{H}_{2}\), and \(\mathrm{NaOH}\) : \(2 \mathrm{NaCl}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \underset{2 \mathrm{NaOH}(a q)}{\longrightarrow}+\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g)\) If the plant produces \(1.5 \times 10^{6} \mathrm{~kg}\left(1500\right.\) metric tons) of \(\mathrm{Cl}_{2}\) daily, estimate the quantities of \(\mathrm{H}_{2}\) and \(\mathrm{NaOH}\) produced.

(a) Determine the chemical formula of the product formed when the metallic element calcium combines with the nonmetallic element oxygen, \(\mathrm{O}_{2}\). Write the balanced chemical equation for the reaction. (b) What products form when a compound containing \(\mathrm{C}, \mathrm{H}\), and \(\mathrm{O}\) is completely combusted in air? Write a balanced chemical equation for the combustion of acetone, \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}(I)\), in air.

(a) Diamond is a natural form of pure carbon. How many moles of carbon are in a \(1.25\) -carat diamond (1 carat \(=0.200 \mathrm{~g}\) )? How many atoms are in this diamond? (b) The molecular formula of acetylsalicylic acid (aspirin), one of the most common pain relievers, is \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\). How many moles of \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) are in a \(0.500-\mathrm{g}\) tablet of aspirin? How many molecules of \(\mathrm{C}_{9} \mathrm{H}_{6} \mathrm{O}_{4}\) are in this tablet?

(a) The characteristic odor of pineapple is due to ethyl butyrate, a compound containing carbon, hydrogen, and oxygen. Combustion of \(2.78 \mathrm{mg}\) of ethyl butyrate produces \(6.32 \mathrm{mg}\) of \(\mathrm{CO}_{2}\) and \(2.58 \mathrm{mg}\) of \(\mathrm{H}_{2} \mathrm{O}\). What is the empirical formula of the compound? (b) Nicotine, a component of tobacco, is composed of \(\mathrm{C}, \mathrm{H}\), and \(\mathrm{N}\). \(\mathrm{A}\) 5.250-mg sample of nicotine was combusted, producing \(14.242 \mathrm{mg}\) of \(\mathrm{CO}_{2}\) and \(4.083 \mathrm{mg}\) of \(\mathrm{H}_{2} \mathrm{O}\). What is the empirical formula for nicotine? If nicotine has a molar mass of \(160 \pm 5 \mathrm{~g} / \mathrm{mol}\), what is its molecular formula?

The fermentation of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) produces ethyl alcohol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) and \(\mathrm{CO}_{2}\) $$ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q) \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q)+2 \mathrm{CO}_{2}(g) $$ (a) How many moles of \(\mathrm{CO}_{2}\) are produced when \(0.400\) mol of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) reactsin this fashion? (b) How many grams of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) are needed to form \(7.50 \mathrm{~g}\) of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} ?\) (c) How many grams of \(\mathrm{CO}_{2}\) form when \(7.50 \mathrm{~g}\) of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) are produced?
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