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Chapter 16: Problem 18

A 28.2 L volume of \(\mathrm{HCl}(\mathrm{g}),\) measured at \(742 \mathrm{mmHg}\) and \(25.0^{\circ} \mathrm{C},\) is dissolved in water. What volume of \(\mathrm{NH}_{3}(\mathrm{g}),\) measured at \(762 \mathrm{mmHg}\) and \(21.0^{\circ} \mathrm{C},\) must be absorbed by the same solution to neutralize the HCl?

Short Answer

Expert verified
The calculated volume of NH3 required to neutralize the HCl is the solution.

Step by step solution

01

Convert HCl Conditions to find Moles

First convert the given pressure of \(742 \, \mathrm{mmHg}\) to atmospheres, because the Ideal Gas Law works with pressures in atmospheres. The conversion factor is \(1 \, \mathrm{atm} = 760 \, \mathrm{mmHg}\). Also, temperatures must be in Kelvin for the Ideal Gas Law. Convert \(25.0^{\circ} \mathrm{C}\) to Kelvin using the relation \(K = ^{\circ} \mathrm{C} + 273.15\). Then, apply the Ideal Gas Law: \(PV = nRT\). Rearrange this formula to \(n = PV/RT\), where P is the pressure in atmospheres, V is the volume in liters, R is the gas constant in \(L \cdot atm / (K \cdot mol)\), and T is the temperature in Kelvin
02

Convert NH3 Conditions to find Volume

The neutralization reaction shows one mole of NH3 is required to neutralize one mole of HCl. So the amount of moles of NH3 required is the same. Now to find the volume of this quantity of NH3, it is necessary to use the Ideal Gas law again. But first, the conditions for NH3 must be converted. The pressure is given as \(762 \, \mathrm{mmHg}\), and should be converted to atmospheres. The temperature is given as \(21.0^{\circ} \mathrm{C}\), and should be converted to Kelvin. To apply the Ideal Gas Law to get V, rearrange to \(V = nRT/P\)
03

Calculate Final Volume

Substitute the number of moles of NH3 obtained from Step 1, and the converted values of P, R and T into the formula. Solve this to get the final volume of NH3 gas.

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Most popular questions from this chapter

It is possible to write simple equations to relate \(\mathrm{pH}\) \(\mathrm{p} K,\) and molarities \((\mathrm{M})\) of various solutions. Three such equations are shown here. $$\begin{aligned} &\text {Weak acid: } \quad \mathrm{pH}=\frac{1}{2} \mathrm{pK}_{\mathrm{a}}-\frac{1}{2} \log \mathrm{M}\\\ &\text { Weak base: } \mathrm{pH}=14.00-\frac{1}{2} \mathrm{pK}_{\mathrm{b}}+\frac{1}{2} \log \mathrm{M} \end{aligned}$$ Salt ofweak \(\operatorname{acid}\left(\mathrm{pK}_{\mathrm{a}}\right)\) and strong base: \(\quad \mathrm{pH}=14.00-\frac{1}{2} \mathrm{pK}_{\mathrm{w}}+\frac{1}{2} \mathrm{p} K_{\mathrm{a}}+\frac{1}{2} \log \mathrm{M}\) (a) Derive these three equations, and point out the assumptions involved in the derivations. (b) Use these equations to determine the pH of 0.10 \(\mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}(\mathrm{aq}), 0.10 \mathrm{M} \mathrm{NH}_{3}(\mathrm{aq}),\) and \(0.10 \mathrm{M}\) \(\mathrm{NaCH}_{3} \mathrm{COO} .\) Verify that the equations give correct results by determining these pH values in the usual way.

Write the formula of the conjugate base in the reaction of each acid with water. (a) \(\mathrm{HIO}_{3} ;\) (b) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\) (c) \(\mathrm{HPO}_{4}^{2-} ;\) (d) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}\)

Of the following, the amphiprotic ion is (a) \(\mathrm{HCO}_{3}^{-}\) (b) \(\mathrm{CO}_{3}^{2-} ;\) (c) \(\mathrm{NH}_{4}^{+} ;\) (d) \(\mathrm{CH}_{3} \mathrm{NH}_{3}^{+} ;\) (e) \(\mathrm{ClO}_{4}^{-}\).

Briefly describe each of the following ideas or phenomena: (a) conjugate base; (b) percent ionization of an acid or base; (c) self-ionization; (d) amphiprotic behavior.

Complete the following equations in those instances in which a reaction (hydrolysis) will occur. If no reaction occurs, so state. (a) \(\mathrm{NH}_{4}^{+}(\mathrm{aq})+\mathrm{NO}_{3}^{-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O} \longrightarrow\) (b) \(\mathrm{Na}^{+}(\mathrm{aq})+\mathrm{NO}_{2}^{-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O} \longrightarrow\) (c) \(\mathrm{K}^{+}(\mathrm{aq})+\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}^{-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O} \longrightarrow\) (d) \(\mathrm{K}^{+}(\mathrm{aq})+\mathrm{Cl}^{-}(\mathrm{aq})+\mathrm{Na}^{+}(\mathrm{aq})+\mathrm{I}^{-}(\mathrm{aq})+\) (e) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}(\mathrm{aq})+\mathrm{Cl}^{-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{H}_{2} \mathrm{O} \longrightarrow\)
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