Problem 2

In a gaseous mixture of CO and

\ce{CO2}

, a mass ratio of carbon : oxygen = 1 : 2 was determined. 2.1 Calculate the mass percent composition of the mixture. 2.2 Calculate the volume percent composition. 2.3 Indicate the values of the carbon : oxygen mass ratio for which both gases cannot be present simultaneously in the mixture.

Step 4 of 4: Forbidden C:O ratios

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\tfrac{m_C}{m_O} = \tfrac{12}{16}\;(\text{pure } \ce{CO})\quad\text{or}\quad \tfrac{12}{32}\;(\text{pure } \ce{CO2})

Analysis

The mass ratio $m_C/m_O$ is a weighted average of the pure-component ratios $12/16$ (CO) and $12/32$ ( $\ce{CO2}$ ). Any intermediate value can arise from a genuine mixture, but the extreme values $12/16$ and $12/32$ correspond to a single pure gas — at those ratios both gases cannot be present simultaneously.

Common pitfall. The ratio 1:2 lies between 12/32 and 12/16, so a mixture is possible — but a ratio outside the interval [12/32, 12/16] would be impossible altogether, not merely 'one gas'.