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Chapter 5: Problem 114

A certain hydrate has the formula \(\mathrm{MgSO}_{4} \cdot x \mathrm{H}_{2} \mathrm{O}\). A quantity of \(54.2 \mathrm{~g}\) of the compound is heated in an oven to drive off the water. If the steam generated exerts a pressure of 24.8 atm in a \(2.00-\mathrm{L}\) container \(\mathrm{at}\) \(120^{\circ} \mathrm{C},\) calculate \(x\)

Short Answer

Expert verified
The value of \(x\) is the moles of water per mol of \(MgSO_4\), calculated by dividing \(n_{H_2O}\) by no. of moles of \(MgSO_4\).

Step by step solution

01

Use Ideal Gas Law to find the number of moles

First, the problem gives you the pressure, volume, and temperature of the steam generated by the water in the hydrate. Utilize these to find the number of moles (\(n\)) of water expelled. Use the Ideal Gas Law: \(PV=nRT\), where \(P\) is pressure in Atm, \(V\) is volume in liters, \(R\) is the gas constant, and \(T\) is temperature in Kelvin. Remember to convert Celsius to Kelvin by adding 273.15.
02

Compute for moles of water

Plug the values into the formula: \(n= PV/RT = (24.8\, atm \times 2.00\,L) / (0.0821\, L\cdot atm/mol\cdot K \times 393.15\, K)\) to get the number of moles of steam and therefore also of water, as each water molecule creates a single water vapor molecule when it evaporates.
03

Determine mass of hydrate before heating

The question mentions that before heating, the weight of the hydrate was 54.2 g.
04

Calculate mass of dehydrated compound

After heating, the remaining compound is \(MgSO_4\). We can find its molecular weight: \(Mg\)=24.305g/mol, \(S\)=32.06g/mol, four \(O\)'s=4*16.00g/mol. Add these values, 24.305+32.06+64.00=120.365g/mol.
05

Deduce mass of water lost

Subtract the mass of the \(MgSO_4\) from the initial mass of the hydrate to get the mass of water that was driven off during heating.
06

Find moles of water lost

Calculate the moles of water lost using its molar mass (18.00 g/mol), let's denote it as \(n_{H_2O}\). Calculate from the obtained mass of water.
07

Compute for x

Finally, determine the number of moles of water that were initially bound to each mole of \(MgSO_4\) by dividing the moles of water obtained by number of moles of \(MgSO_4\). This gives you the number \(x\) in the hydrate's formula \(MgSO_4 \cdot xH_2O\).

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Most popular questions from this chapter

The density of a mixture of fluorine and chlorine gases is \(1.77 \mathrm{~g} / \mathrm{L}\) at \(14^{\circ} \mathrm{C}\) and 0.893 atm. Calculate the mass percent of the gases.

Describe how you would measure, by either chemical or physical means, the partial pressures of a mixture of gases of the following composition: (a) \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2,}(\mathrm{~b}) \mathrm{He}\) and \(\mathrm{N}_{2}\)

Which of the following statements is correct? (a) Heat is produced by the collision of gas molecules against one another. (b) When a gas is heated, the molecules collide with one another more often.

Consider the formation of nitrogen dioxide from nitric oxide and oxygen: $$ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) $$ If \(9.0 \mathrm{~L}\) of \(\mathrm{NO}\) are reacted with excess \(\mathrm{O}_{2}\) at \(\mathrm{STP}\), what is the volume in liters of the \(\mathrm{NO}_{2}\) produced?

Calculate the density of hydrogen bromide (HBr) gas in grams per liter at \(733 \mathrm{mmHg}\) and \(46^{\circ} \mathrm{C}\).
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