Evaluate or simplify the expression without using a calculator.
-The $\mathrm { pH }$ of a solution ranges from 0 to 14 . An acid has a pH less than 7 . Pure water is neutral and has a pH of 7. The $\mathrm { pH }$ of a solution is given by $\mathrm { pH } = - \log x$ where $x$ represents the concentration of the hydrogen ions in the solution in moles per liter. Find the $\mathrm { pH }$ if the hydrogen ion concentration is $6.4 \times 10 ^ { - 3 }$.
A) $2.19$
B) $3.81$
C) $3.19$
D) $2.81$

Question

Quizplus · Accepted Answer

The pH is calculated using the formula $\mathrm { pH } = - \log x$. Plugging in $x = 6.4 \times 10 ^ { - 3 }$, we get $\mathrm { pH } = - \log (6.4 \times 10 ^ { - 3 })$. Without a calculator, we estimate the log value, knowing that $\log (1 \times 10^{-3}) = -3$ and $\log (1 \times 10^{-2}) = -2$, so $\log (6.4 \times 10^{-3})$ is between -3 and -2, closer to -2 because 6.4 is closer to 10 than to 1. Thus, the pH is slightly above 2, making 2.19 the most reasonable estimate.

Evaluate or Simplify the Expression Without Using a Calculator pH\mathrm { pH }pH

Evaluate or Simplify the Expression Without Using a Calculator $\mathrm { pH }$