Chemistry

Problem

A classroom measures

8.0\,\text{m}\times6.0\,\text{m}\times3.0\,\text{m}

and is completely sealed during a short experiment. Take the density of air as

1.2\,\text{kg}\,\text{m}^{-3}

, the molar mass of air as

29\,\text{g}\,\text{mol}^{-1}

and Avogadro’s number as

6.02\times10^{23}\,\text{mol}^{-1}

. Using these values, find the order of magnitude of the number of air molecules present in the room. Work out your answer in the steps given below. a. (i) Calculate the volume of air enclosed in the room. b. (ii) Determine the mass of the enclosed air. c. (iii) Estimate the number of air molecules present and state its order of magnitude.

Intuitive explanation

This problem asks you to connect the macroscopic world—a room's volume and air's density—to the microscopic world of individual molecules. The key insight is to work through three conversions in sequence: volume to mass (using density), mass to moles (using molar mass), and moles to molecules (using Avogadro's number). Each step is a straightforward multiplication, so focus on keeping track of units and powers of 10 to find the final order of magnitude.

Intuitive explanation

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