A tomato has a proton concentration of 0.00006 M.How would you calculate the pH? log (6 x 10-5) b) log (6 x 10-5) log (6 x 105) log (0.006) x 5
The Correct Answer and Explanation is:
Step-by-Step:
Given:[H+]=0.00006 M=6×10−5 M[H^+] = 0.00006 \, \text{M} = 6 \times 10^{-5} \, \text{M}[H+]=0.00006M=6×10−5M
Apply the pH formula:pH=−log(6×10−5)\text{pH} = -\log(6 \times 10^{-5})pH=−log(6×10−5)
Use logarithmic rules:pH=−[log(6)+log(10−5)]\text{pH} = -[\log(6) + \log(10^{-5})]pH=−[log(6)+log(10−5)]=−[log(6)−5]=−log(6)+5= -[\log(6) – 5] = -\log(6) + 5=−[log(6)−5]=−log(6)+5log(6)≈0.778\log(6) \approx 0.778log(6)≈0.778
So:pH=−0.778+5=4.22\text{pH} = -0.778 + 5 = 4.22pH=−0.778+5=4.22
Correct Answer:
pH ≈ 4.22
Explanation
pH is a measure of the acidity or basicity of a solution and is defined as the negative logarithm of the hydrogen ion concentration:pH=−log[H+]\text{pH} = -\log[H^+]pH=−log[H+]
This logarithmic scale means that each unit change in pH reflects a tenfold change in [H+][H^+][H+]. A lower pH value corresponds to a higher concentration of hydrogen ions, indicating a more acidic solution.
In this example, the tomato has a proton (hydrogen ion) concentration of 0.00006 M, which is written in scientific notation as 6×10−56 \times 10^{-5}6×10−5 M. Plugging this into the pH formula gives:pH=−log(6×10−5)\text{pH} = -\log(6 \times 10^{-5})pH=−log(6×10−5)
To simplify, we use properties of logarithms:log(ab)=log(a)+log(b)\log(ab) = \log(a) + \log(b)log(ab)=log(a)+log(b)
So:log(6×10−5)=log(6)+log(10−5)=log(6)−5\log(6 \times 10^{-5}) = \log(6) + \log(10^{-5}) = \log(6) – 5log(6×10−5)=log(6)+log(10−5)=log(6)−5
Then:pH=−(log(6)−5)=−log(6)+5\text{pH} = -(\log(6) – 5) = -\log(6) + 5pH=−(log(6)−5)=−log(6)+5
Since log(6)≈0.778\log(6) \approx 0.778log(6)≈0.778, the final pH is approximately:pH=−0.778+5=4.22\text{pH} = -0.778 + 5 = 4.22pH=−0.778+5=4.22
Thus, the tomato’s pH is about 4.22, which is acidic. This is consistent with real-world observations, as tomatoes are known to be slightly acidic. Understanding how to calculate pH from proton concentration is fundamental in chemistry and biology, especially for analyzing natural substances like fruits.
