Example 3 A sample of orange juice has a Hydrogen ion concentration of 2.9times 10^-4M . What is the pH ?

To find the pH of the orange juice sample, we can use the formula for pH, which is:<br /><br />\[ \text{pH} = -\log[\text{H}^+] \]<br /><br />where \([\text{H}^+]\) is the hydrogen ion concentration in moles per liter (M).<br /><br />Given:<br />\[ [\text{H}^+] = 2.9 \times 10^{-4} \, \text{M} \]<br /><br />Now, plug this value into the pH formula:<br /><br />\[ \text{pH} = -\log(2.9 \times 10^{-4}) \]<br /><br />Using a calculator to find the logarithm:<br /><br />\[ \text{pH} = -(\log(2.9) + \log(10^{-4})) \]<br />\[ \text{pH} = -(\log(2.9) - 4) \]<br />\[ \text{pH} = 4 - \log(2.9) \]<br /><br />Using a calculator to find \(\log(2.9)\):<br /><br />\[ \log(2.9) \approx 0.462 \]<br /><br />So,<br /><br />\[ \text{pH} = 4 - 0.462 \]<br />\[ \text{pH} \approx 3.538 \]<br /><br />Therefore, the pH of the orange juice sample is approximately 3.54.