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Chapter 4: Problem 106

A small piece of zinc is dissolved in \(50.00 \mathrm{mL}\) of \(1.035 \mathrm{M}\) HCl. At the conclusion of the reaction, the concentration of the \(50.00 \mathrm{mL}\) sample is redetermined and found to be \(0.812 \mathrm{M} \mathrm{HCl} .\) What must have been the mass of the piece of zinc that dissolved? $$\mathrm{Zn}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) \longrightarrow \mathrm{ZnCl}_{2}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g})$$

Short Answer

Expert verified
The mass of the piece of zinc that dissolved is approximately \(0.364 \, \text{grams}\).

Step by step solution

01

Calculate Initial Moles of Hydrochloric Acid

The initial moles of hydrochloric acid are obtained by multiplying the initial concentration by the volume (Expressed in litres). Which equals to \(1.035 \, \text{M} \times 0.05 \, \text{L} = 0.05175 \, \text{mol}\).
02

Calculate Final Moles of Hydrochloric Acid

Similar to the first step, calculate the final moles of hydrochloric acid. Multiply the final concentration by the volume: \(0.812 \, \text{M} \times 0.05 \, \text{L} = 0.0406 \, \text{mol}\).
03

Calculate Moles of Zinc

The reaction between zinc and hydrochloric acid is a 1:2 reaction, meaning 1 mole of zinc reacts with 2 moles of hydrochloric acid. So, the moles of zinc that reacted would be half of the moles of hydrochloric acid that reacted. Therefore, subtract the final moles of HCl from the initial moles to get the moles of HCl that reacted and divide by 2 to get the moles of zinc that reacted: \((0.05175 - 0.0406) \, \text{mol} / 2 = 0.005575 \, \text{mol}\).
04

Find Mass of Zinc

Finally, convert moles of zinc to grams using the molar mass of zinc (65.38 g/mol): \(0.005575 \, \text{mol} \times 65.38 \, \text{g/mol} = 0.364 \, \text{g}\).

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Most popular questions from this chapter

Iron ore is impure \(\mathrm{Fe}_{2} \mathrm{O}_{3} .\) When \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) is heated with an excess of carbon (coke), metallic iron and carbon monoxide gas are produced. From a sample of ore weighing \(938 \mathrm{kg}, 523 \mathrm{kg}\) of pure iron is obtained. What is the mass percent \(\mathrm{Fe}_{2} \mathrm{O}_{3},\) by mass, in the ore sample, assuming that none of the impurities contain Fe?

The incomplete combustion of gasoline produces \(\mathrm{CO}(\mathrm{g})\) as well as \(\mathrm{CO}_{2}(\mathrm{g}) .\) Write an equation for \((\mathrm{a})\) the complete combustion of the gasoline component octane, \(\mathrm{C}_{8} \mathrm{H}_{18}(\mathrm{l}),\) and \((\mathrm{b})\) incomplete combustion of octane with \(25 \%\) of the carbon appearing as \(\mathrm{CO}(\mathrm{g})\)

Water and ethanol, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(\mathrm{l}),\) are miscible, that is, they can be mixed in all proportions. However, when these liquids are mixed, the total volume of the resulting solution is not equal to the sum of the pure liquid volumes, and we say that the volumes are not additive. For example, when \(50.0 \mathrm{mL}\) of water and \(50.0 \mathrm{mL}\) of \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(\mathrm{l}),\) are mixed at \(20^{\circ} \mathrm{C},\) the total volume of the solution is \(96.5 \mathrm{mL}\), not \(100.0 \mathrm{mL}\). (The volumes are not additive because the interactions and packing of water molecules are slightly different from the interactions and packing of \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) molecules.) Calculate the molarity of \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) in a solution prepared by mixing \(50.0 \mathrm{mL}\) of water and \(50.0 \mathrm{mL}\) of \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(\mathrm{l})\) at \(20^{\circ} \mathrm{C} .\) At this temperature, the densities of water and ethanol are 0.99821 \(\mathrm{g} / \mathrm{mL}\) and \(0.7893 \mathrm{g} / \mathrm{mL},\) respectively.

For a specific reaction, ammonium dichromate is the only reactant and chromium(III) oxide and water are two of the three products. What is the third product and how many grams of this product are produced per kilogram of ammonium dichromate decomposed?

Consider the reaction below: \(2 \mathrm{AgNO}_{3}(\mathrm{aq})+\mathrm{Na}_{2} \mathrm{S}(\mathrm{aq}) \longrightarrow\) $$ \mathrm{Ag}_{2} \mathrm{S}(\mathrm{s})+2 \mathrm{NaNO}_{3}(\mathrm{aq}) $$ (a) How many grams of \(\mathrm{Na}_{2} \mathrm{S}(\mathrm{s})\) are required to react completely with \(27.8 \mathrm{mL}\) of \(0.163 \mathrm{M} \mathrm{AgNO}_{3} ?\) (b) How many grams of \(\mathrm{Ag}_{2} \mathrm{S}(\mathrm{s})\) are obtained from the reaction in part (a)?
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