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A 4.36 -g sample of an unknown alkali metal hydroxide is dissolved in 100.0 \(\mathrm{mL}\) of water. An acid-base indicator is added, and the resulting solution is titrated with 2.50 \(\mathrm{M} \mathrm{HCl}(a q)\) solution. The indicator changes color, signaling that theequivalence point has been reached, after 17.0 \(\mathrm{mL}\) of the hydrochloric acid solution has been added. (a) What is the molar mass of the metal hydroxide? (b) What is the identity of the alkalimetal cation: \(\mathrm{Li}^{+}, \mathrm{Na}^{+}, \mathrm{K}^{+}, \mathrm{Rb}^{+},\) or \(\mathrm{Cs}^{+} ?\)

Short Answer

Expert verified
The molar mass of the unknown alkali metal hydroxide (MOH) is approximately 40 g/mol. Based on the comparison with the molar masses of the known alkali metal hydroxides, the identity of the alkali metal cation is Na鈦 (sodium).

Step by step solution

01

Find the moles of HCl

: We are given the concentration (2.50 M) and volume (17.0 mL) of the HCl solution. To find the moles of HCl, we can use the formula: moles = concentration 脳 volume Since the volume is given in milliliters, we need to convert it to liters by dividing by 1000. \(moles_{HCl} = (2.50 \, \mathrm{M}) \times (17.0 \, \mathrm{mL} \times \frac{1 \, \mathrm{L}}{1000 \, \mathrm{mL}}) \)
02

Find the moles of MOH

: At the equivalence point, the moles of HCl and MOH are equal (1:1 ratio). Therefore, \(moles_{MOH} = moles_{HCl}\).
03

Calculate the molar mass of MOH

: We are given the mass of MOH (4.36 g), and we found the moles of MOH in step 2. To calculate the molar mass, use the formula: \(molar \, mass_{MOH} = \frac{mass_{MOH}}{moles_{MOH}}\). Substitute the known values in the formula and calculate the molar mass.
04

Identify the alkali metal cation

: Compare the calculated molar mass of MOH with the molar masses of known alkali metal hydroxides (LiOH, NaOH, KOH, RbOH, and CsOH). The cation with the closest molar mass to the calculated molar mass will be the identity of the alkali metal cation in the unknown hydroxide.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molar Mass Calculation
Understanding the molar mass of a substance is crucial for various chemical calculations. Molar mass is the mass of one mole of a substance and is usually expressed in grams per mole (g/mol). It is the sum of the atomic masses of all atoms in a molecule. To calculate the molar mass, you will use the formula:
\[\begin{equation}\text{Molar Mass} = \frac{\text{Total Mass of Compound}}{\text{Number of Moles}}\text{.}\end{equation}\]In an acid-base titration scenario, after finding the number of moles of the titrant (in this case, HCl), you can then compute the molar mass of the unknown substance by dividing the mass of the unknown by the number of moles of the titrant, assuming a 1:1 ratio at the equivalence point.

When the substance is an unknown alkali metal hydroxide, the process includes the additional step of obtaining the substance's mass first, which then enables you to proceed with the calculation. It is important to convert the volume of solutions to liters and note that all substances involved in calculations are pure, without impurities, for accurate molar mass determination.
Alkali Metal Hydroxide Identification
In the context of acid-base titrations, identifying an unknown alkali metal hydroxide involves comparing the calculated molar mass of the metal hydroxide with the known molar masses of common alkali metal hydroxides: LiOH, NaOH, KOH, RbOH, and CsOH. Each alkali metal has a distinctive molar mass.

Once you have the molar mass from the titration data, you check which known alkali metal hydroxide's molar mass closely matches your calculated value. Careful measurement and calculation are vital in this step to avoid misidentification. An alkali metal hydroxide is composed of an alkali metal cation and the hydroxide anion, and their combined atomic/ionic masses give the molar mass of the hydroxide.
Stoichiometry
Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. In a titration, stoichiometry helps you understand the proportions in which reactants combine. In the case of acid-base titrations, the reaction typically occurs with a 1:1 mole ratio. Therefore, the moles of acid (HCl, in our example) will equal the moles of the base (MOH) at the equivalence point.

Understanding stoichiometry allows you to make predictions about the outcome of a reaction and calculate unknown concentrations, which is particularly important when working with solutions in a titration experiment. It provides the foundation for understanding the equivalence point and is especially significant in determining the concentration of an unknown solution through titration.
Equivalence Point
The equivalence point in a titration is the moment when the quantity of titrant added is stoichiometrically equivalent to the quantity of substance present in the sample. For acid-base titrations, this is when moles of acid equal moles of base. A pH indicator or a pH meter can signal when the equivalence point is reached through a change in color or a specific pH measurement, respectively.

The significance of the equivalence point extends beyond indicating when stoichiometric amounts of reactants have been mixed. It enables chemists to calculate unknown concentrations, as seen in the process of identifying an unknown alkali metal hydroxide. Correctly interpreting the equivalence point is critical for accurate titrimetric analysis and subsequent calculations, such as molar mass determination and substance identification.

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Most popular questions from this chapter

The concept of chemical equilibrium is very important. Which one of the following statements is the most correct way to think about equilibrium? (a) If a system is at equilibrium, nothing is happening. (b) If a system is at equilibrium, the rate of the forward reaction is equal to the rate of the back reaction. (c) If a system is at equilibrium, the product concentration is changing over time. Section 4.1\(]\)

Indicate the concentration of each ion or molecule present in the following solutions: (a) 0.25\(M\) NaNO \(_{3}\) , (b) \(1.3 \times 10^{-2} M \mathrm{MgSO}_{4},(\mathbf{c}) 0.0150 M \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},(\mathbf{d})\) a mixture of 45.0 \(\mathrm{mL}\) of 0.272 \(\mathrm{M} \mathrm{NaCl}\) and 65.0 \(\mathrm{mL}\) of 0.0247 \(\mathrm{M}\) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3} .\) Assume that the volumes are additive.

(a) By titration, 15.0 \(\mathrm{mL}\) of 0.1008 \(\mathrm{M}\) sodium hydroxide is needed to neutralize a \(0.2053-\mathrm{g}\) sample of a weak acid. What is the molar mass of the acid if it is monoprotic? (b) An elemental analysis of the acid indicates that it is composed of \(5.89 \% \mathrm{H}, 70.6 \% \mathrm{C},\) and 23.5\(\% \mathrm{O}\) by mass. What is composed of \(5.89 \% \mathrm{H}, 70.6 \% \mathrm{C},\) and 23.5\(\% \mathrm{O}\) by mass. What is its molecular formula?

Bronze is a solid solution of \(\mathrm{Cu}(\mathrm{s})\) and \(\mathrm{Sn}(\mathrm{s})\) ; solutions of metals like this that are solids are called alloys. There is a range of compositions over which the solution is considered a bronze. Bronzes are stronger and harder than either copper or tin alone. (a) \(\mathrm{A} 100.0\) -g sample of a certain bronze is 90.0\(\%\) copper by mass and 10.0\(\%\) tin. Which metal can be called the solvent, and which the solute? (b) Based on part (a), calculate the concentration of the solute metal in the alloy in units of molarity, assuming a density of 7.9 \(\mathrm{g} / \mathrm{cm}^{3}\) . (c) Suggest a reaction that you could do to remove all the tin from this bronze to leave a pure copper sample. Justify your reasoning.

Magnesium carbonate, magnesium oxide, and magnesium hydroxide are all white solids that react with acidic solutions. (a) Write a balanced molecular equation and a netionic equation for the reaction that occurs when each substance reacts with a hydrochloric acid solution. (b) By observing the reactions in part (a), how could you distinguish any of the three magnesium substances from the other two?

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