The pH scale is logarithmic, meaning every whole number change on the scale reflects a ten-fold change in acidity. Since a pH of 3 is three numbers higher than a pH of 6, we can find the change in acidity by taking 10 to the third power.

The solution with a pH of 3 is 1000 times more acidic than the solution with a pH of 6. 

Since hydrochloric acid is considered a strong acid, we can assume that the acid will dissociate completely, leaving us with a 0.03M concentration of hydronium ions. Knowing this, we can calculate the pH by taking the negative log of the hydronium concentration:

To solve this question we need to first look at the relationship between hydroxide and hydrogen ion concentrations:

where  is concentration of hydrogen ions and  is the concentration of hydroxide ions. Solve for :

We can solve for the concentration of hydrogen ions in this solution by writing the dissociation of hydrochloric acid in solution:

The question states that it is a 1M solution. Since  and  are in 1:1 ratio, the concentration of hydrogen ions will equal the concentration ; therefore, . Note that this won’t be the case if the acid was weak. For a weak acid, the concentration of  will be less than the concentration of acid, even if it was 1:1 ratio. This occurs because a weak acid does not dissociate completely.

We can now use the  to solve for .

Therefore, concentration of hydroxide ions in this solution is

Recall that acids and bases can be defined in three different ways. First, the Arrhenius definition states that an acid is a substance that increases the concentration of hydrogen ions in solution whereas a base decreases hydrogen ions concentration. Second, Bronsted-Lowry definition states that an acid is any substance that donates a proton whereas a base is any substance that accepts a proton. Finally, Lewis definition states that an acid is any substance that accepts an electron pair whereas a base is a substance that donates an electron pair.

We have two substances in this question. , or borane, is considered a Lewis acid because it accepts an electron pair. Boron has four orbitals in its outermost shell. If we look at Boron in borane, we will notice that three orbitals are occupied by the electrons in the three single bonds (bound to hydrogen) whereas the last orbital is empty and is free to accept electrons. Since it accepts electrons, borane is considered a lewis acid. , or ammonia, is a lewis base. If we look at the nitrogen atom in ammonia, we will notice that all of its orbitals are occupied (three orbitals are occupied with the three bonds to hydrogen atoms and the last orbital is occupied with a lone electron pair). Since it has extra electrons in the last orbital, ammonia can donate electrons and is considered a lewis base.

The question states that the  of solution A is higher. The definition of  is:

If we rearrange and solve for concentration of hydroxide ions, we get

This means that  decreases as  increases. The relationship between hydroxide ion and hydrogen ion is as follows

Note that the hydroxide ion concentration is inversely proportional to that of hydrogen ions; therefore, lower hydroxide ion concentration leads to higher hydrogen ion concentration and higher acidity. Since solution A has the higher , its hydroxide ion concentration is lower than solution B. This means that solution A has higher hydrogen ion concentration and, therefore, is more acidic than solution B.

The question also states that the  of solution B is lower. Recall that as  of an acid decreases it becomes more acidic. Based on this, we conclude that solution B is more acidic. The two results given in this question conflict each other; therefore, these results seem invalid.

Acid dissociation constant, or , for a prototypical acid-base reaction is defined as

where  is an acid and  is its conjugate base. Based on this equation, we can determine that  and  are directly proportional to one another; therefore, increasing  will increase  and vice versa.

Recall the definition of 

Solving for  gives us

This means that increasing pH will decrease  and vice versa (has the opposite effect on each other); therefore,  and  also have an opposite effect on each other.

The buffer is made by using weak acid and its conjugate base. The relationship between the concentration of the components (acid and conjugate base), pKa, and pH can be determined by using the Henderson-Hasselbalch equation.

where  is weak acid and  is the conjugate base. We know that equal amounts of  and  are added; therefore,  for buffer solutions made in this manner. To calculate the pKa of the solution we need the pH.

Hydrochloric acid () and sodium hydroxide () are both strong reagents. Adding equal amounts of strong acid to a strong base neutralizes the solution and gives the solution a neutral pH of 7. This means that the concentration of hydrogen ions and hydroxide ions are equal to each other. If pH was greater than 7 (basic pH), then the hydroxide ion concentration would be higher and if pH was less than 7 (acidic pH) then hydrogen ion concentration would be higher.

Solution A has two weak reagents whereas solution B contains a strong base. This means that solution B will be more basic, will have a higher concentration of hydroxide ions, and a higher pH.  is a constant and is not altered by the relative reagents (it is always equal to ). Recall that pOH is defined as

This equation suggests that pOH decreases as the hydroxide ion concentration increases. Since it has the higher hydroxide ion concentration, solution B will have a lower pOH.

Since this problem involves both the acid and the conjugate base of the acid, we can use the Henderson-Hasselbach equation in order to determine the pH of the solution: