How would you estimate the number of gas molecules in one cubic meter of air in the classroom on an average day?

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How would you estimate the number of gas molecules in one cubic meter of air in the classroom on an average day?

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Answer 1 · 2016-05-11T07:40:42

We would use the molar volume of an ideal gas at $SLC$ $"SLC"$ as an approximation. There are are approx 41 moles of air, thus $41 \cdot m o l \times N_{A}$ $41*molxxN_A$ $=$ $=$ $number of gas molecules$ $"number of gas molecules"$

Explanation:

Given the molar volume, we know that 1 mole of an ideal gas occupies $24.5 \cdot L$ $24.5*L$ at $SLC$ $"SLC"$ , i.e. the molar volume is $24.5 \cdot L \cdot m o l^{- 1}$ $24.5*L*mol^-1$ .

Knowing that $1$ $1$ $m^{3}$ $m^3$ $=$ $=$ $1000 \cdot L$ $1000*L$ we simply divide this quantity by the first:

$Number of moles$ $"Number of moles"$ $=$ $=$ $\frac{1000 \cdot L}{24.5 \cdot L \cdot m o l^{- 1}}$ $(1000*L)/(24.5*L*mol^-1)$ $=$ $=$ $41 \cdot moles$ $41*"moles"$

Each mole of gas contains $N_{A}$ $N_A$ gas molecules, whose behaviour is assumed to be ideal.

Thus, $number of gas molecules$ $"number of gas molecules"$ $41 \cdot m o l \times N_{A}$ $41*molxxN_A$ $=$ $=$ $41 \cdot m o l \times 6.022 \times 10^{23} \cdot m o l^{- 1}$ $41*molxx6.022xx10^23*mol^-1$ .

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How would you estimate the number of gas molecules in one cubic meter of air in the classroom on an average day?

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