Question: pH and corresponding hydrogen ion concentration
Q. Answer this question by filling in the blanks in the following paragraph:
The higher the hydrogen ion concentration ($[H^+]$), the ___ the pH.
Ideal gas law equation
The following equation is commonly used to describe the state of an ideal gas:
$pV = nRT$
Glossary of terms used in this equation:
$p$ = pressure (pascals)
$V$ = Volume (m^3)
$n$ = amount of gas (moles)
$R$ = the ideal gas constant (8.3145 J\cdot K^{-1}\cdot mol^{-1})
$T$ = Temperature (K)
1. **State the problem:** We need to understand the relationship between hydrogen ion concentration $[H^+]$ and pH.
2. **Recall the formula for pH:**
$$\text{pH} = -\log_{10} [H^+]$$
This means pH is the negative logarithm (base 10) of the hydrogen ion concentration.
3. **Interpret the formula:**
- If $[H^+]$ increases, then $\log_{10} [H^+]$ increases.
- Since pH is the negative of this logarithm, an increase in $[H^+]$ causes pH to decrease.
4. **Answer the blank:**
The higher the hydrogen ion concentration ($[H^+]$), the **lower** the pH.
5. **Additional information:**
The ideal gas law equation $pV = nRT$ relates pressure, volume, amount of gas, gas constant, and temperature, but it is unrelated to pH or hydrogen ion concentration.
**Final answer:** The higher the hydrogen ion concentration ($[H^+]$), the lower the pH.