# Video: Calculating the K(sp) of AgBr Given the Concentration of Ag⁺ Ions in a Saturated Solution at 25°C

A saturated solution of AgBr at 25°C contains 7 × 10⁻⁷ moles per liter of Ag⁺ ions. What is the Ksp value of this salt? [A] 4.9 × 10⁻¹⁵ [B] 4.9 × 10⁻¹⁴ [C] 7 × 10⁻¹⁴ [D] 4.9 × 10⁻¹³ [E] 7 × 10⁻⁷

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### Video Transcript

A saturated solution of AgBr at 25 degrees Celsius contains seven times 10 to the minus seven moles per liter of Ag+ ions. What is the Ksp value of this salt? (A) 4.9 times 10 to the minus 15. (B) 4.9 times 10 to the minus 14. (C) Seven times 10 to the minus 14. (D) 4.9 times 10 to the minus 13. (E) Seven times 10 to the minus seven.

When you introduce a solid salt to water such as AgBr or silver bromide like we have in this question, the salt will begin to dissolve and break up into the ions that it’s composed of. In this case, silver bromide would break up into silver cations and bromide anions. The salt will continue to dissolve until the solution is saturated with ions, at which point the solution cannot contain any more of the dissolved solute.

This process is temperature dependent, which is why the temperature is specified in this question. When you have a higher temperature, more solute is able to dissolve in the solution than when there’s a lower temperature.

You may have noticed that the process of dissolution is an equilibrium reaction, which means we can create an equilibrium expression to figure out how much of the dissolved ions the solution can contain when it’s saturated. This equilibrium expression will be equal to the equilibrium constant for this process, which is the Ksp. And it will be equal to the concentration of the dissolved ions raised to the power of their stochiometric coefficients. So, the Ksp for this reaction will be equal to the concentration of silver ions in the solution times the concentration of bromide ions in the solution.

We’re given the concentration of silver ions in the solution in the problem. It’s seven times 10 to the minus seven moles per liter. But what is the concentration of the bromide ions in the solution? Well, according to our balanced chemical equation for the dissolution of silver bromide, every one mole of silver bromide that dissolves will give us one mole of silver ions and one mole of bromide ions. In other words, the concentration of the silver ions and the bromide ion should be equal in our solution.

So, we have everything that we need to solve for the Ksp for silver bromide. We just need to multiply seven times 10 to the minus seven by seven times 10 to the minus seven to find our answer. Seven times seven gives us 49. And when we multiply exponents that have the same base, we can quickly figure out what they’re equal to by adding the values in their exponents. So, negative seven plus negative seven gives us 10 to the negative 14.

Now, we have our answer, but it’s not in scientific notation. So, we’ll need to move the decimal place over by one. This would increase the value in the exponent by one. So, our final answer is 4.9 times 10 to the minus 13, which matches answer choice (D). So, the Ksp value for silver bromide is 4.9 times 10 to the minus 13.