Hydrogen peroxide is used as a cleansing agent in the treatment of cuts and abrasions for several reasons. It is an oxidizing agent that can directly kill many microorganisms; it decomposes on contact with blood, releasing elemental oxygen gas (which inhibits the growth of anaerobic microorganisms); and it foams on contact with blood, which provides a cleansing action. In the laboratory, small quantities of hydrogen peroxide can be prepared by the action of an acid on an alkaline earth metal peroxide, such as barium peroxide: $$ \mathrm{BaO}_{2}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{BaCl}_{2}(a q) $$ What mass of hydrogen peroxide should result when \(1.50 \mathrm{~g}\) barium peroxide is treated with \(25.0 \mathrm{~mL}\) hydrochloric acid solution containing \(0.0272 \mathrm{~g} \mathrm{HCl}\) per \(\mathrm{mL}\) ? What mass of which reagent is left unreacted?

Step by step solution

01

Calculate moles of barium peroxide and hydrochloric acid

We need to first convert the mass of barium peroxide and the volume of hydrochloric acid into moles. To do this, divide the mass by the molar mass for each substance: Moles of barium peroxide: \( moles_{BaO2} = \frac{mass_{BaO2}}{molar\,mass_{BaO2}}=\frac{1.50\,g}{(137.327+2×16)\,g/mol}=\frac{1.50\,g}{169.327\,g/mol} = 0.008864\,mol \) Moles of hydrochloric acid: \( moles_{HCl}=volume_{HCl}\times concentration_{HCl}=25.0\,mL\times\frac{0.0272\,g}{mL}\times\frac{1\,mol}{36.461\,g}= 0.01862\,mol \)

02

Identify the limiting reagent

The balanced equation shows that 1 mole of barium peroxide reacts with 2 moles of hydrochloric acid. To determine the limiting reagent, we need to compare the mole ratios: \( \frac{moles_{BaO2}}{moles_{HCl}} = \frac{0.008864\,mol}{0.01862\,mol} = 0.4761 < 0.5 \) Since the ratio is less than 0.5, Barium peroxide is the limiting reagent.

03

Calculate the moles of hydrogen peroxide formed

Now we can use the balanced equation to calculate moles of hydrogen peroxide produced: \( moles_{H2O2} = moles_{BaO2} \times \frac{1\,mol\,H2O2}{1\,mol\,BaO2} = 0.008864\,mol \)

04

Convert moles of hydrogen peroxide to mass

Next, convert the moles of hydrogen peroxide to mass by multiplying with its molar mass: \( mass_{H2O2} = moles_{H2O2}\times molar\,mass_{H2O2} = 0.008864\,mol\times(2×1.00784+2×16)\,g/mol = 1.52\,g \)

05

Calculate the mass of unreacted reagent

Since barium peroxide is the limiting reagent, all of it reacts. To find the unreacted hydrochloric acid, we need to calculate how much of it reacted and then subtract it from the initial amount: Moles of reacted hydrochloric acid: \( moles_{reacted\,HCl} = moles_{BaO2} \times \frac{2\,mol\,HCl}{1\,mol\,BaO2} = 0.008864\,mol\times 2 = 0.01773\,mol \) Mass of unreacted hydrochloric acid: \( mass_{unreacted\,HCl} = (moles_{HCl} - moles_{reacted\,HCl})\times molar\,mass_{HCl} \) \( mass_{unreacted\,HCl} = (0.01862\,mol - 0.01773\,mol)\times 36.461\,g/mol = 0.0324\,g \) So the mass of hydrogen peroxide formed is \(1.52\,g\) and the unreacted mass of hydrochloric acid is \(0.0324\,g\).

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