Question 2.2: Calculating the Mass of an Element in a Compound Problem Pit......
Calculating the Mass of an Element in a Compound
Problem Pitchblende is the most important compound of uranium. Mass analysis of an 84.2-g sample of pitchblende shows that it contains 71.4 g of uranium, with oxygen the only other element. How many grams of uranium and of oxygen are in 102 kg of pitchblende?
Plan We have to find the masses (in g) of uranium and of oxygen in a known mass (102 kg) of pitchblende, given the mass of uranium (71.4 g) in a different mass of pitchblende (84.2 g) and knowing that oxygen is the only other element present. The mass ratio of uranium to pitchblende in grams is the same as it is in kilograms. Therefore, using Equation 2.1, we multiply the mass (in kg) of the pitchblende sample by the ratio of uranium to pitchblende (in kg) from the mass analysis. This gives the mass (in kg) of uranium, and we convert kilograms to grams. To find the mass of oxygen, the only other element in the pitchblende, we subtract the calculated mass of uranium (in kg) from the given mass of pitchblende (102 kg) and convert kilograms to grams.
Solution Finding the mass (kg) of uranium in 102 kg of pitchblende:
\text{Mass (kg) of uranium = mass (kg) of pitchblende} \times \frac{\text{mass (kg) of uranium in pitchblende}}{\text{mass (kg) of pitchblende}}
= 102 \cancel{\text{kg pitchblende}} \times \frac{\text{71.4 kg uranium}}{84.2 \cancel{\text{kg pitchblende}}} = 86.5 \text{kg uranium}
Converting the mass of uranium from kg to g:
\text{Mass (g) of uranium = 86.5 } \cancel{kg} \text{ uranium} \times \frac{1000 g}{1 \cancel{kg}} = 8.65 \times 10^4 \text{g uranium}Finding the mass (in kg) of oxygen in 102 kg of pitchblende:
Converting the mass of oxygen from kg to g:
\text{Mass (g) of oxygen = 15.5 } \cancel{kg} \text{ oxygen} \times \frac{1000 g}{1 \cancel{kg}} = 1.55 \times 10^4 \text{g oxygen}Check The analysis showed that most of the mass of pitchblende is due to uranium, so the large mass of uranium makes sense. Rounding off to check the math gives
\text{∼100 kg pitchblende} \times \frac{70}{85} = 82 \text{kg uranium}