Question

Please explain procedure. The first-order decay of radon has a half-life of 3.823 days. How many grams of radon remain after 7.22 days if the sample initially weighs 250.0 grams?

Answer #1

**Given:**

**Half life = 3.823 days**

**All decays are 1st order reaction**

**use relation between rate constant and half life of 1st
order reaction**

**k = (ln 2) / k**

**= 0.693/(half life)**

**= 0.693/(3.823)**

**= 0.1813 days-1**

**we have:**

**[Radon]o = 250.0 gram**

**t = 7.22 days**

**k = 0.1813 days-1**

**Given:**

**[Radon]o = 250 M**

**use integrated rate law for 1st order
reaction**

**ln[Radon] = ln[Radon]o - k*t**

**ln[Radon] = ln(250) - 0.1813*7.22**

**ln[Radon] = 5.521461 - 0.1813*7.22**

**ln[Radon] = 4.212682**

**[Radon] = 67.54 grams**

**Answer: 67.54 grams**

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