This is a simple case of ratios. `(1 mol)/(22.4 L)=(n mol)/(.025 L)` Then we cross multiply and we get `22.4n=.025` We divide each side by 22.4 to find `n=.001116 mol` Then to convert the moles to atoms we multiply, and cross-cancel the units `(.001116 mol)/1 xx (6.02 xx 10^23 atms)/(1...

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This is a simple case of ratios. `(1 mol)/(22.4 L)=(n mol)/(.025 L)` Then we cross multiply and we get `22.4n=.025` We divide each side by 22.4 to find `n=.001116 mol` Then to convert the moles to atoms we multiply, and cross-cancel the units `(.001116 mol)/1 xx (6.02 xx 10^23 atms)/(1 mol)` and we have `6.72 xx 10^20` atoms. I've found the trick of cross-cancelling units to be a very effective mnemonic, it always makes sure you carry out the correct calculation to find the desired units.