An iron meteorite was analysed for its isotopic argon content. The amount of was (STP) per kg of met — States of Matter and Gaseous State Chemistry Question
Question
An iron meteorite was analysed for its isotopic argon content. The amount of $\text{Ar}^{36}$ was $1.911 \text{ mm}^3$ (STP) per kg of meteorite. If each $\text{Ar}^{36}$ atom had been formed by a single cosmic event, how many such events must there have been per kg of meteorite? If the answer is $X$, then the value of $X/10^{16}$ is ($R = 8.4 \text{ J/K-mol}$, $N_A = 6.0 \times 10^{23}$)
💡 Solution & Explanation
STP implies $T = 273\text{ K}$, $P = 10^5\text{ Pa}$ (using given $R=8.4$). Volume $V = 1.911 \times 10^{-9} \text{ m}^3$. Moles $n = \frac{PV}{RT} = \frac{10^5 \times 1.911 \times 10^{-9}}{8.4 \times 273} = \frac{1.911 \times 10^{-4}}{2293.2} \approx 8.33 \times 10^{-8} \text{ mol}$. Number of atoms $X = n \times N_A = 8.33 \times 10^{-8} \times 6.0 \times 10^{23} = 5.0 \times 10^{16}$. Thus $X/10^{16} = 5$. Therefore, correct answer is 5.