Samples of pure carbon weighing \(3.62,5.91,\) and \(7.07 \mathrm{g}\) were burned in an excess of air. The masses of carbon dioxide obtained (the sole product in each case) were \(13.26,21.66,\) and \(25.91 \mathrm{g},\) respectively. (a) Do these data establish that carbon dioxide has a fixed composition? (b) What is the composition of carbon dioxide, expressed in \% C and \% O, by mass?

According to the law of definite proportions, if carbon dioxide has a fixed composition, the ratio of the mass of carbon dioxide produced to the mass of carbon used should be the same in all three trials. To confirm this, calculate the ratio for each trial: \[ \text{Ratio} = \frac{\text{Mass of } CO_2}{\text{Mass of Carbon}} \] For the first trial, this will be \(\frac{13.26}{3.62}\), the second trial will be \(\frac{21.66}{5.91}\), and the third trial will be \(\frac{25.91}{7.07}\). If these values are the same or very close to one another, then carbon dioxide does have a fixed composition.

To confirm the composition of carbon dioxide by mass, understanding that a molecule of carbon dioxide (CO2) consists of one atom of carbon and two atoms of oxygen is necessary. Total molecular mass can be calculated by adding the atomic masses of its constituents (from the periodic table): carbon has a mass of 12.01 g/mol and oxygen has a mass of 16.00 g/mol. So total mass of carbon dioxide (CO2) comes to \(12.01+2*(16.00) = 44.01 \mathrm{g/mol}\). \nThen we calculate the mass percent of Carbon (C) in Carbon dioxide (CO2): \[ \text{% C} = \left( \frac{\text{Carbon's mass}}{\text{Total mass}} \right) * 100\% = \left(\frac{12.01}{44.01}\right) * 100\%\] Similarly, calculate the mass percent of Oxygen (O) in Carbon dioxide (CO2): \[ \text{% O} = \left( \frac{\text{Oxygen's mass}}{\text{Total mass}} \right) * 100\% = \left(\frac{2*16.00}{44.01}\right) * 100\%\]