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Chapter 5: Problem 81

A sample of battery acid is to be analyzed for its sulfuric acid content. A \(1.00 \mathrm{mL}\) sample weighs \(1.239 \mathrm{g}\). This \(1.00 \mathrm{mL}\) sample is diluted to \(250.0 \mathrm{mL}\), and \(10.00 \mathrm{mL}\) of this diluted acid requires \(32.44 \mathrm{mL}\) of \(0.00498 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\) for its titration. What is the mass percent of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in the battery acid? (Assume that complete ionization and neutralization of the \(\mathrm{H}_{2} \mathrm{SO}_{4}\) occurs.)

Short Answer

Expert verified
The mass percent of \(H_2SO_4\) in the battery acid is 0.1282%.

Step by step solution

01

Calculate moles of \(Ba(OH)_2\)

First, calculate moles of \(Ba(OH)_2\) used in the reaction. The number of moles (n) can be calculated using the molarity (M) and volume (V), in liter, as n=M*V. Given, M =0.00498M and V=32.44mL =0.03244L, so n=0.00498 * 0.03244 = 0.000162 moles.
02

Calculate moles of \(H_2SO_4\)

Second, we calculate moles of \(H_2SO_4\). According to balanced chemical reaction - \(H_2SO_4 + Ba(OH)_2 -> BaSO_4 + 2H_2O\), 1 mole of \(H_2SO_4\) reacts with 1 mole of \(Ba(OH)_2\), so moles of \(H_2SO_4\) = moles of \(Ba(OH)_2\) = 0.000162 moles. This is moles of \(H_2SO_4\) in 10mL of diluted solution.
03

Calculate moles of \(H_2SO_4\) in 1mL diluted solution

Now, we calculate moles of \(H_2SO_4\) present in 1mL of the diluted solution. If 10mL diluted solution contains 0.000162 moles of \(H_2SO_4\), then 1mL will contain = 0.0000162 moles of \(H_2SO_4\).
04

Calculate mass of \(H_2SO_4\)

The molar mass of \(H_2SO_4\) is 98 g/mol, so the mass of \(H_2SO_4\) in 1mL sample = moles of \(H_2SO_4\) in 1mL * molar mass of \(H_2SO_4\)= 0.0000162 * 98 = 0.0015876 g. This is the mass of \(H_2SO_4\) in 1mL = 1.239g sample of battery acid.
05

Calculate mass percent of \(H_2SO_4\)

Finally, calculate the mass percent of \(H_2SO_4\) in the sample as (mass of \(H_2SO_4\) / mass of sample) * 100 = (0.0015876 / 1.239) * 100 = 0.1282 %. So, the mass percent of \(H_2SO_4\) in the battery acid is 0.1282%.

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Most popular questions from this chapter

Warfarin, \(\mathrm{C}_{19} \mathrm{H}_{16} \mathrm{O}_{4},\) is the active ingredient used in some anticoagulant medications. The amount of warfarin in a particular sample was determined as follows. A 13.96 g sample was first treated with an alkaline I_ solution to convert \(\mathrm{C}_{19} \mathrm{H}_{16} \mathrm{O}_{4}\) to \(\mathrm{CHI}_{3}\). This treatment gives one mole of \(\mathrm{CHI}_{3}\) for every mole of \(\mathrm{C}_{19} \mathrm{H}_{16} \mathrm{O}_{4}\) that was initially present in the sample. The iodine in \(\mathrm{CHI}_{3}\) is then precipitated as \(\mathrm{AgI}(\mathrm{s})\) by treatment with excess \(\mathrm{AgNO}_{3}(\mathrm{aq}):\) $$\begin{aligned} \mathrm{CHI}_{3}(\mathrm{aq})+3 \mathrm{AgNO}_{3}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow & \longrightarrow 3 \mathrm{AgI}(\mathrm{s})+3 \mathrm{HNO}_{3}(\mathrm{aq}) &+\mathrm{CO}(\mathrm{g}) \end{aligned}$$ If \(0.1386 \mathrm{g}\) solid \(\mathrm{AgI}\) were obtained, then what is the percentage by mass of warfarin in the sample analyzed?

Select the (a) best and (b) poorest electrical conductors from the following solutions, and explain the reason for your choices: \(0.10 \mathrm{M} \mathrm{NH}_{3} ; 0.10 \mathrm{M} \mathrm{NaCl} ; 0.10 \mathrm{M}\) \(\mathrm{CH}_{3} \mathrm{COOH}\) (acetic acid); \(0.10 \mathrm{M} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) (ethanol).

Complete each of the following as a net ionic equation. If no reaction occurs, so state. (a) \(\mathrm{Ba}^{2+}+2 \mathrm{OH}^{-}+\mathrm{CH}_{3} \mathrm{COOH} \longrightarrow\) (b) \(\mathrm{H}^{+}+\mathrm{Cl}^{-}+\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH} \longrightarrow\) (c) \(\operatorname{FeS}(\mathrm{s})+\mathrm{H}^{+}+\mathrm{I}^{-} \longrightarrow\) (d) \(\mathrm{K}^{+}+\mathrm{HCO}_{3}^{-}+\mathrm{H}^{+}+\mathrm{NO}_{3}^{-} \longrightarrow\) (e) \(\mathrm{Mg}(\mathrm{s})+\mathrm{H}^{+} \longrightarrow\)

Which solutions would you use to precipitate \(\mathrm{Mg}^{2+}\) from an aqueous solution of \(\mathrm{MgCl}_{2} ?\) Explain your choice. (a) \(\mathrm{KNO}_{3}(\mathrm{aq}) ;\) (b) \(\mathrm{NH}_{3}(\mathrm{aq}) ;\) (c) \(\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq});\) (d) \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(\mathrm{aq})\).

Predict in each case whether a reaction is likely to occur. If so, write a net ionic equation. (a) $\mathrm{HI}(\mathrm{aq})+\mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq}) \longrightarrow$ (b) $\operatorname{CuSO}_{4}(\mathrm{aq})+\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{aq}) \longrightarrow$ (c) $\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})+\mathrm{Na}_{3} \mathrm{PO}_{4}(\mathrm{aq}) \longrightarrow$
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