Question
Question 2 (4 points) a) It is estimated that 20% of a certain radioactive substance decays in 30 hours. What is the half life of this substance? b) If tomato juice with a pH of 4.2 is 75 times more acidic as milk what is the pH of milk? (Recall that lower pH's are more acidic!)
Solution
3.6
(255 Votes)
Abel
Professional · Tutor for 6 years
Answer
**a) Half-life Calculation*** **Understanding Decay:** A 20% decay means 80% (or 0.80) of the substance remains after 30 hours. The general formula for radioactive decay is: N(t) = N₀ * (1/2)^(t/T) Where: * N(t) is the amount remaining after time t * N₀ is the initial amount * t is the elapsed time * T is the half-life* **Setting up the equation:** We can set up the equation using the information given: 0.80 = (1/2)^(30/T)* **Solving for T (half-life):** Take the logarithm of both sides (base 1/2 or base 10 – it doesn't matter as long as you're consistent): log(0.80) = (30/T) * log(1/2) T = 30 * log(1/2) / log(0.80) T ≈ 93.19 hours Therefore, the half-life of the substance is approximately 93.19 hours.**b) pH of Milk Calculation*** **Understanding pH:** The pH scale is logarithmic. A difference of 1 pH unit represents a tenfold difference in acidity. Since the tomato juice is 75 times more acidic than milk, we need to find the pH difference that corresponds to this factor.* **Calculating the pH difference:** 75 is not a perfect power of 10, so we'll use logarithms: pH difference = log₁₀(75) pH difference ≈ 1.88* **Finding the pH of milk:** Since tomato juice is *more* acidic (lower pH), we *add* the pH difference to the pH of tomato juice to find the pH of milk: pH of milk = pH of tomato juice + pH difference pH of milk = 4.2 + 1.88 pH of milk ≈ 6.08 Therefore, the pH of milk is approximately 6.08.