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An unknown salt is either \(\mathrm{NaCN}, \mathrm{NaC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\), NaF, \(\mathrm{NaCl}\), or \(\mathrm{NaOCl}\). When \(0.100 \mathrm{~mol}\) of the salt is dissolved in \(1.00 \mathrm{~L}\) of solution, the \(\mathrm{pH}\) of the solution is \(8.07\). What is the identity of the salt?

Short Answer

Expert verified
The identity of the unknown salt responsible for the given pH of 8.07 is NaOCl, as its dissociation in water provides a significant [OH鈦籡 concentration compared to the other possible salts.

Step by step solution

01

Write the formula for pH and list the given information.

The pH of a solution is given by the formula: \(pH = -\log[H^+] \) We are given the following information: - \(0.100 \ mol\) of salt is dissolved in \(1.00 \ L\) of solution - the pH of the solution is 8.07
02

Calculate the pOH and [OH-] concentration.

Since we know the pH of the solution, use the relation \(pH + pOH = 14\) to find the pOH. \(pOH = 14 - pH\) Substitute the given pH value and solve for pOH: \(pOH = 14 - 8.07 = 5.93\) Now, calculate the [OH鈦籡 concentration using the formula: \([OH^-] = 10^{-pOH}\) Substitute the pOH value and find the [OH鈦籡 concentration: \([OH^-] = 10^{-5.93} = 1.17 \times 10^{-6} M \)
03

Write the ionization equations for each salt and analyze their effect on the [OH鈦籡 concentration.

For each salt, write the equation for how it ionizes in water and identify which ion(s) will increase the [OH鈦籡 concentration. 1) NaCN: \(NaCN \rightarrow Na^+ + CN^-\) (CN鈦 acts as a weak base) 2) NaC鈧侶鈧僌鈧: \(NaC_2H_3O_2 \rightarrow Na^+ + C_2H_3O_2^-\) (C鈧侶鈧僌鈧傗伝 acts as a weak base) 3) NaF: \(NaF \rightarrow Na^+ + F^-\) (F鈦 acts as a weak base) 4) NaCl: \(NaCl \rightarrow Na^+ + Cl^-\) (Cl鈦 does not affect the [OH鈦籡 concentration) 5) NaOCl: \(NaOCl \rightarrow Na^+ + OCl^-\) (OCl鈦 acts as a weak base) We can eliminate NaCl from contention since it does not affect the [OH鈦籡 concentration, and the pH of the solution is above 7, which indicates a basic solution. Now we will use the [OH鈦籡 concentration to find which salt matches the given pH.
04

Use the [OH鈦籡 concentration to determine the ion which causes the pH.

Use the [OH鈦籡 concentration to calculate the concentration of the corresponding anions (weak bases). Since all of the salts were dissolved in 1L of solution, we can equate their moles to molarity. 1) CN鈦: The dissociation of CN鈦 will produce a very small [OH鈦籡 concentration as it is a weak base. Comparing it with the given [OH鈦籡 concentration, it won't match, so CN鈦 is not the reason behind the given pH. 2) C鈧侶鈧僌鈧傗伝: Similarly, the dissociation of C鈧侶鈧僌鈧傗伝 will also produce a very small [OH鈦籡 concentration compared to the given value, so it's not the reason behind the given pH. 3) F鈦: In this case, the dissociation of F鈦 will produce a significant [OH鈦籡 concentration compared to CN鈦 and C鈧侶鈧僌鈧傗伝 as F鈦 is less weak relative to them. However, the [OH鈦籡 concentration produced is also very small compared to the given value. So, F鈦 is not the reason behind the given pH. 4) OCl鈦: The dissociation of OCl鈦 will produce a significant [OH鈦籡 concentration compared to the other weak bases. Since OCl鈦 is less weak relative to the other weak bases, it could be responsible for producing the given [OH鈦籡 concentration. Given the above analysis, we can conclude that the salt causing the given pH is:
05

Conclusion

The identity of the salt responsible for the given pH is NaOCl.

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Key Concepts

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

pOH and pH Relationship
Understanding the relationship between pH and pOH is crucial when dealing with acid-base chemistry. The scale of pH measures the acidity of a solution, indicating its hydrogen ion concentration (ol[H^+]). The pOH, on the other hand, measures the basicity of a solution, reflecting its hydroxide ion concentration (ol[OH^-]). The pH and pOH of a solution are inversely related and add up to 14 at 25掳C, due to the self-ionization of water. This is expressed in the equationol[ pH + pOH = 14 ].
When given the pH of a solution, one can easily determine the pOH by subtracting the pH from 14. Hence, if a solution has a pH of 8.07, the pOH can be calculated asol[ pOH = 14 - 8.07 = 5.93 ]. With the pOH known, we can further calculate the concentration of hydroxide ions usingol[ [OH^-] = 10^{-pOH} ], which is integral to identifying the influence of various salts in an aqueous solution.
Weak Base Ionization
Ionization of weak bases in water plays an important role in determining the pH of the resulting solution. A weak base partially ionizes in solution, and this process is influenced by the base's strength. In the exercise, we encountered several salts that when dissolved in water, their anions acted as weak bases. For instance, the anion CN鈦 from NaCN, the anion C鈧侶鈧僌鈧傗伝 from NaC鈧侶鈧僌鈧, and F鈦 from NaF are examples of such ions.
The extent of ionization of a weak base is much lower than that of a strong base, leading to a lower concentration of hydroxide ions. In a solution of 1L, the number of moles of a salt is equal to its molarity. From the given pH or [OH鈦籡 concentration, it is possible to gauge the extent of ionization by comparing the calculated [OH鈦籡 against expected values for known weak bases. The weak base that would result in an [OH鈦籡 concentration closest to the calculated value from the problem could be identified as the one responsible for the pH of the solution.
Identifying Unknown Salts
Identifying unknown salts based on pH involves an understanding of their ionization behavior in water. In the provided problem, we are to deduce the identity of the salt from the measured pH of the solution. Each salt, when dissolved, dissociates to give a particular anion which may act as a acidic or basic species. The chloride ion (Cl鈦), for example, is a neutral ion, and hence, a salt like NaCl would not raise the pH above 7, thus can be eliminated as a candidate if the solution is basic.
The approach to identifying the salt involves calculating the [OH鈦籡 concentration from the given pH and matching it with the expected hydroxide ion yield from the ionization of the various anions. This process requires understanding of acid-base strength and the salts' reactivity in water. The salt that can produce the closest hydroxide ion concentration to the calculated one is determined to be the unknown salt in question, leading to the conclusion in the textbook exercise.

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