Questions: If the half-life of I-131 is 25.4 days, how many moles of I-131 would be left in Mr. Miller's body after 68 days if he was infused with 5.6 grams? (Round your answer to four decimal places)

Solution Steps

First, we need to calculate the initial number of moles of I-131. The molar mass of I-131 is approximately 130.9061 g/mol. Given that Mr. Miller was infused with 5.6 grams of I-131, we can calculate the initial moles using the formula:

\[ \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} \]

\[ \text{Moles} = \frac{5.6 \, \text{g}}{130.9061 \, \text{g/mol}} \approx 0.0428 \, \text{mol} \]

The half-life of I-131 is 25.4 days. We need to determine how many half-lives have passed in 68 days:

\[ \text{Number of Half-Lives} = \frac{68 \, \text{days}}{25.4 \, \text{days/half-life}} \approx 2.6772 \]

The amount of a substance remaining after a certain number of half-lives can be calculated using the formula:

\[ N = N_0 \left(\frac{1}{2}\right)^n \]

where \(N_0\) is the initial amount, \(n\) is the number of half-lives, and \(N\) is the remaining amount.

\[ N = 0.0428 \, \text{mol} \times \left(\frac{1}{2}\right)^{2.6772} \approx 0.0067 \, \text{mol} \]

Final Answer