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Chapter 5: Problem 108

The volume of a sample of pure HCl gas was \(189 \mathrm{~mL}\) at \(25^{\circ} \mathrm{C}\) and \(108 \mathrm{mmHg} .\) It was completely dissolved in about \(60 \mathrm{~mL}\) of water and titrated with an \(\mathrm{NaOH}\) solution; \(15.7 \mathrm{~mL}\) of the \(\mathrm{NaOH}\) solution were required to neutralize the \(\mathrm{HCl}\). Calculate the molarity of the \(\mathrm{NaOH}\) solution.

Short Answer

Expert verified
The molarity of the NaOH solution is \(0.57 \text{ M}\).

Step by step solution

01

Calculate the moles of HCl gas

The moles of a gas can be calculated using the Ideal Gas Law, \(PV = nRT\), where P represents pressure, V volume, n the number of moles, R the ideal gas constant, and T the temperature in Kelvin. Converting given temperature to Kelvin (25°C + 273 = 298 K) and pressure to atm (108 mmHg / 760 mmHg = 0.142 atm), we solve the equation for n: \[n = \frac{PV}{RT} = \frac{0.142 \times 0.189}{0.0821 \times 298} = 0.00896 \text{ moles}\]
02

Find the neutralization reaction

HCl reacts with NaOH to form water and NaCl in a 1:1 ratio: \(HCl + NaOH \rightarrow H_2O + NaCl\). The number of moles of NaOH needed to neutralize HCl equals the number of moles of HCl. Therefore, 0.00896 moles of NaOH were used.
03

Calculate the molarity of NaOH solution

Molarity (M) is defined as the number of moles of solute per liter of solution. Converting the volume of NaOH solution used to liters (15.7 mL = 0.0157 L), the molarity can be computed as: \[M = \frac{n}{V} = \frac{0.00896}{0.0157} = 0.57 \text{ M}\]

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Most popular questions from this chapter

A mixture of calcium carbonate \(\left(\mathrm{CaCO}_{3}\right)\) and magnesium carbonate \(\left(\mathrm{MgCO}_{3}\right)\) of mass \(6.26 \mathrm{~g}\) reacts completely with hydrochloric acid (HCl) to generate \(1.73 \mathrm{~L}\) of \(\mathrm{CO}_{2}\) at \(48^{\circ} \mathrm{C}\) and 1.12 atm. Calculate the mass percentages of \(\mathrm{CaCO}_{3}\) and \(\mathrm{MgCO}_{3}\) in the mixture.

A student breaks a thermometer and spills most of the mercury (Hg) onto the floor of a laboratory that measures \(15.2 \mathrm{~m}\) long, \(6.6 \mathrm{~m}\) wide, and \(2.4 \mathrm{~m}\) high. (a) Calculate the mass of mercury vapor (in grams) in the room at \(20^{\circ} \mathrm{C}\). The vapor pressure of mercury at \(20^{\circ} \mathrm{C}\) is \(1.7 \times 10^{-6} \mathrm{~atm} .\) (b) Does the concentration of mercury vapor exceed the air quality regulation of \(0.050 \mathrm{mg} \mathrm{Hg} / \mathrm{m}^{3}\) of air? (c) One way to treat small quantities of spilled mercury is to spray sulfur powder over the metal. Suggest a physical and a chemical reason for this action.

Nitrous oxide \(\left(\mathrm{N}_{2} \mathrm{O}\right)\) can be obtained by the thermal decomposition of ammonium nitrate \(\left(\mathrm{NH}_{4} \mathrm{NO}_{3}\right) .\) (a) Write a balanced equation for the reaction. (b) In a certain experiment, a student obtains \(0.340 \mathrm{~L}\) of the gas at \(718 \mathrm{mmHg}\) and \(24^{\circ} \mathrm{C}\). If the gas weighs \(0.580 \mathrm{~g},\) calculate the value of the gas constant.

Apply your knowledge of the kinetic theory of gases to the following situations. (a) Two flasks of volumes \(V_{1}\) and \(V_{2}\left(V_{2}>V_{1}\right)\) contain the same number of helium atoms at the same temperature. (i) Compare the root-mean-square (rms) speeds and average kinetic energies of the helium (He) atoms in the flasks. (ii) Compare the frequency and the force with which the He atoms collide with the walls of their containers. (b) Equal numbers of He atoms are placed in two flasks of the same volume at temperatures \(T_{1}\) and \(T_{2}\left(T_{2}>T_{1}\right) .\) (i) Compare the rms speeds of the atoms in the two flasks. (ii) Compare the frequency and the force with which the He atoms collide with the walls of their containers. (c) Equal numbers of He and neon (Ne) atoms are placed in two flasks of the same volume, and the temperature of both gases is \(74^{\circ} \mathrm{C}\). Comment on the validity of the following statements: (i) The rms speed of He is equal to that of Ne. (ii) The average kinetic energies of the two gases are equal. (iii) The rms speed of each He atom is \(1.47 \times 10^{3} \mathrm{~m} / \mathrm{s}\)

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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