The pH level, [tex]$P$[/tex], of a liquid can be determined from the hydronium ion [tex]$\left( H _2 O ^{+}\right)$[/tex] concentration, c, using the equation [tex]$P=- log ( c )$[/tex]. If the pH level of grape juice is 3.3, what is the hydronium Ion concentration?
A. [tex]$501 \times 10^{-4}$[/tex]
B. [tex]$1.19 \times 10^{-2}$[/tex]
C. [tex]$1.99 \times 10^3$[/tex]
D. [tex]$153 \times 10^4$[/tex]
Answer (2)
Substitute the given pH level into the equation: 3.3 = − l o g ( c ) .
Solve for c by taking the inverse logarithm: c = 1 0 − 3.3 .
Calculate the value: c ≈ 0.000501187 .
Express the answer in scientific notation: 501 × 1 0 − 4 .
Explanation
Understanding the Problem We are given the equation P = − l o g ( c ) , where P is the pH level and c is the hydronium ion concentration. We are also given that the pH level of grape juice is 3.3, so P = 3.3 . We need to find the hydronium ion concentration, c .
Solving for c Substitute the given value of P into the equation: 3.3 = − l o g ( c ) Multiply both sides by -1: − 3.3 = l o g ( c ) Since the base of the logarithm is not specified, we assume it is base 10. Rewrite the equation in exponential form: c = 1 0 − 3.3
Calculating the Concentration Calculate the value of 1 0 − 3.3 . c = 1 0 − 3.3 ≈ 0.000501187 Now we need to express this value in scientific notation to match the given answer choices. c ≈ 5.01187 × 1 0 − 4 Comparing this to the given options, we see that the closest answer is 501 × 1 0 − 4 .
Final Answer Therefore, the hydronium ion concentration is approximately 501 × 1 0 − 4 .
Examples
Understanding pH levels is crucial in many real-world applications. For example, in agriculture, knowing the pH of the soil helps farmers determine the best crops to grow and the necessary soil treatments. In medicine, maintaining the correct pH balance in the body is essential for various biological processes. In environmental science, monitoring the pH of water sources helps assess pollution levels and ensure water safety. The formula P = − l o g ( c ) allows us to quantify acidity and alkalinity, enabling informed decisions in these diverse fields.
The hydronium ion concentration of grape juice with a pH level of 3.3 is calculated using the formula c = 1 0 − 3.3 , resulting in approximately 501 × 1 0 − 4 . Therefore, the answer is option A. This means the hydronium ion concentration is about 0.000501 in standard form.
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