### 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.