One way of separating oxygen isotopes is by gaseous diffusion of carbon monoxide. The gaseous diffusion process behaves like an effusion process. Calculate the relative rates of effusion of \({ }^{12} \mathrm{C}^{16} \mathrm{O},{ }^{12} \mathrm{C}^{17} \mathrm{O}\), and \({ }^{12} \mathrm{C}^{18} \mathrm{O}\). Name some advan- tages and disadvantages of separating oxygen isotopes by gaseous diffusion of carbon dioxide instead of carbon monoxide.

Calculate the molar masses of the three isotopes of carbon monoxide by summing the atomic masses of the carbon and oxygen atoms. We will use the atomic mass unit (u) for the calculation: - \({ }^{12} \mathrm{C}^{16}\mathrm{O}\): \(12 u + 16 u = 28 u\) - \({ }^{12} \mathrm{C}^{17}\mathrm{O}\): \(12 u + 17 u = 29 u\) - \({ }^{12} \mathrm{C}^{18}\mathrm{O}\): \(12 u + 18 u = 30 u\)

Graham's Law of Effusion states that the rate of effusion of two gases is inversely proportional to the square root of their molar masses: \(\frac{Rate_1}{Rate_2} = \sqrt{\frac{M_2}{M_1}}\). We can use this formula to compare the rates of effusion of the three isotopes: Relative rate of effusion of \({ }^{12} \mathrm{C}^{16}\mathrm{O}\) to \({ }^{12} \mathrm{C}^{17}\mathrm{O}\): \(\frac{Rate_{16}}{Rate_{17}} = \sqrt{\frac{29u}{28u}} \approx 1.035\) Relative rate of effusion of \({ }^{12} \mathrm{C}^{16}\mathrm{O}\) to \({ }^{12} \mathrm{C}^{18}\mathrm{O}\): \(\frac{Rate_{16}}{Rate_{18}} = \sqrt{\frac{30u}{28u}} \approx 1.069\)

Separating oxygen isotopes by gaseous diffusion of carbon dioxide instead of carbon monoxide could have the following advantages and disadvantages: Advantages: 1. Carbon dioxide is less toxic, making the process safer for workers. 2. Carbon dioxide is a more stable molecule, which could lead to fewer complications or side reactions during the process. Disadvantages: 1. The molar masses of the isotopes would be higher in the case of carbon dioxide, which could lead to smaller differences in relative effusion rates, making the separation process more challenging or less efficient. 2. Carbon dioxide might be less reactive with certain materials, making it potentially more difficult to separate the isotopes after the diffusion process. In conclusion, the relative rates of effusion of \({ }^{12} \mathrm{C}^{16}\mathrm{O}\), \({ }^{12} \mathrm{C}^{17}\mathrm{O}\), and \({ }^{12} \mathrm{C}^{18}\mathrm{O}\) are approximately 1:0.965:0.931. While using carbon dioxide instead of carbon monoxide for the separation process has some advantages, it might also lead to a less efficient separation due to smaller differences in relative effusion rates.