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How does acid and bases affect $pH$?

Answer
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Hint:Use relation of $pH$ and ${H^ + }$to find the effect of acids and bases. Acids will increase the concentration of ${H^ + }$ ions while on the other hand bases decreases ${H^ + }$ concentration. A decrease in concentration of ${H^ + }$ ion will increase the $pH$ and if there is an increase in ${H^ + }$ concentration the $pH$ decreases.

Complete answer:
Both acidity and basicity is termed according to the concentration of hydrogen ions in their solutions. There are in total three theories which give the different definitions of acids and bases. So if we consider the first theory it will suggest that an acid is a solution which gives ${H^ + }$ ions in solution or increases the concentration of these ions. While on the other we can say bases are the substance which decrease the concentration of ${H^ + }$ or increase the concentration of ${}^ - OH$ ions.
Now we get what acids and bases and how there is an increase in concentrations of hydrogen ion. Now let’s see what will happen if these ions get increased or decrease on $pH$ .
We know from our classes that $pH$ and ${H^ + }$ are connected by a formula, which we can write it as $pH = - \log \left[ {{H^ + }} \right]$ , here if concentration of ${H^ + }$ increases then overall value get negative and at last $pH$ get decrease. On the other hand, if the concentration of ${H^ + }$ decreases having a negative value, at the end the overall value increases and we get a positive value at last for$pH$.
Now let’s understand this concept by taking an example of hydrochloric acid $HCl$ and sodium hydroxide $NaOH$. Suppose we take water in a beaker and then we are adding $HCl$ drop by drop, by this drop by drop concentration of ${H^ + }$ increases in the beaker because acid gives ${H^ + }$ in the solution thus by applying this relation $pH = - \log \left[ {{H^ + }} \right]$ overall $pH$ get decrease. In the scale of $1$ to $14$ acid gets $pH$below $6$ . On the other hand if we take $NaOH$ in the beaker and put it drop by drop, it will give hydroxide ions in the solution ${}^ - OH$ or we can say concentration of ${}^ - OH$ increases and concentration of ${H^ + }$ decreases. By the above relation we now get it that the overall $pH$increases and gave a positive value, so in case of bases their $pH$ remain greater than $7$ in scale of $1 - 14$

Note: We should keep in mind that while putting the values in the relation of $pH$ and ${H^ + }$ concentration which is $pH = - \log \left[ {{H^ + }} \right]$ , always put concentration in units of (M) molarity. Calculate the value of $(\log )$ not $(\ln )$ because we always have confusion between the two $(\log )$ is in base $(10)$ while $(\ln )$ is in base $(e)$.