Given the hydroxide ion concentration, we will need to work using pOH to find the pH. We know that the sum of pH and pOH is equal to 14.

Use our value for the concentration to find the pOH.

Now that we have the pOH, we can use it to solve for the pH.

Since HCN is a weak acid, we must use the equilibrium equation.

Because the HCN dissociates in solution, we expect the concentrations of protons and cyanide ions to increase, while the concentration of HCN will decrease. After determining the molarity of the solution, we can set up the equation below, using X as the amount of moles that dissociate.

Because X is small, we can neglect its impact in the denominator.

Since X is the concentration of protons in the solution, we can calculate the pH by using the equation .

The MCAT will typically allow you to approximate the difference in pH between two solutions. Look at the problem this way: you should already know a proton concentration of 1 * 10^-3M means a pH of 3. You do not need to know the exact pH of 5 * 10^-6M, but you should recognize that it is in between 1 * 10^-6M and 1 * 10^-5M. This means it will have a pH between 5 and 6.

The difference in pH will therefore be between 5 minus 3 and 6 minus 3.

As a result, look for the answer that is between 2 and 3. The only answer that makes sense is 2.3.

The equation to calculate pH is:

The normal pH of arterial blood is around 7.4. This reflects a concentration of hydrogen ions that can be found using the pH equation.

Using similar calculations for the second blood sample, we can find the hydrogen ion concentration again.

Now that we have both concentrations, can find the ratio of the acidity of the two samples.

You may know from biological sciences that this is approaching a lethal level of acidosis.

 is a strong acid, meaning it will completely dissociate in solution. As such, the concentration of the acid will be equal to the proton concentration. Thus, to find pH, you should just plug the molar concentration of the acid solution into the pH formula.

A buffer must contain either a weak base and its salt or a weak acid and its salt. A mixture of ammonia and ammonium chloride is an example of the first case, since ammonia, NH₃, is a weak base and ammonium chloride, NH₄Cl, contains its salt.

Though autoionization of water produces small amounts of H₃O⁺ and OH^-, each conjugate salts of H₂O, they exist in such small amounts as to make any buffering effects negligible.

First, we need to determine from both the information presented in the paragraph and the chemical equation what HCO₃^- is doing. The paragraph tells us “HCO₃^- also [serves] to control the pH of the blood.” This is the definition of a buffer. A buffer is able to mitigate the addition of acid or base to a solution, or in this case, blood, by being deprotonated or protonated. For example, if the blood becomes too acidic, H⁺ will recombine with HCO₃^- to form H₂CO₃, thus stabilizing the pH. Alternatively, if the pH becomes too basic, H₂CO₃ will dissociate, releasing H⁺ into solution.

Whenever a concentration of the conjugate base is initially present in the solution, we say that the solution has been buffered. NaCN will completely dissolve in solution, meaning that there will be 1M of CN^- ions in the solution initially (one mole of NaCN in 1L of soultion equals 1M). With this in mind, the new equilibrium equation for the acid's dissociation is as follows:

The initial concentrations of CN^- and HCN are given in the question as 1M and 2M, respectively. The initial concentration of H⁺ is zero. As HCN begine to dissociate, H⁺ and CN^- will each increase by X amount, while HCN will decrease by X amount.

Since 1M and 2M are much larger numbers than the value for X, the X values next to these numbers can be omitted from the equation.

By plugging this value into the equation , we determine that the pH of the solution is 8.9. (Remember that X is equal to the amount of increase in H⁺ ions).

This may seem wrong, because HCN is an acid, and we are used to acids resulting in solutions with pH values less than 7; however, HCN is a weak acid, and a large concentration of its conjugate base can result in a basic solution.

In a buffered solution, when the concentrations of acid and conjugate base are equal, we know the .

This is derived from the Henderson-Hasselbalch equation: .

When concentrations are equal, the log of  is , and .

In our question, the pH is approximately one unit greater than the .

Because of this, we know that the log of the two concentrations must be equal to one.

The log of  is , and therefore the conjugate base must be ten times greater than the acid; therefore the ratio of acid to base is approximately .

We can quickly narrow this question to two possible answers, since the buffered solution is more basic than the , and thus we would expect there to be a greater concentration of base than acid in the solution.

A buffer is best made of equal and copious amounts of an acid and its conjugate base. The acid must have a pK_a as close as possible to the pH desired. For this question, the desired pH is 6. The best option will have a pK_a of about 5.9.

Adding larger amounts of the acid than the base will skew the equilibrium in favor of the acid, increasing the overall proton concentration, and limiting the buffer ability to absorb more proton addition without changing pH significantly.