Question

The mineral uraninite is a uranium oxide that is \(84.80 \%\) uranium by mass. Show calculations to determine the correct empirical formula of uraninite.

Short answer

The empirical formula of uraninite is \(U_3O_8\).

Step-by-step solution

Define Known Values

Given that uraninite is 84.80% uranium by mass, this implies that the remaining 15.20% of uraninite's mass is oxygen.

Assume a Sample Mass

Assume we have a 100 g sample of uraninite. This will make the calculations straightforward. In a 100 g sample, there are 84.80 g of uranium and 15.20 g of oxygen.

Calculate Moles of Uranium

The molar mass of uranium (U) is approximately 238 g/mol. Calculate the moles of uranium in the sample: \[ \text{Moles of U} = \frac{84.80 \text{ g}}{238 \text{ g/mol}} \approx 0.356 \text{ mol} \]

Calculate Moles of Oxygen

The molar mass of oxygen (O) is approximately 16 g/mol. Calculate the moles of oxygen in the sample: \[ \text{Moles of O} = \frac{15.20 \text{ g}}{16 \text{ g/mol}} = 0.950 \text{ mol} \]

Determine the Simplest Whole Number Ratio

Divide the number of moles of each element by the smallest number of moles calculated:- \( \frac{0.356}{0.356} = 1 \) for uranium- \( \frac{0.950}{0.356} \approx 2.67 \) for oxygenSince 2.67 is roughly 8/3, multiply both ratios by 3 to get whole numbers:- Uranium: \(1 \times 3 = 3\)- Oxygen: \(2.67 \times 3 \approx 8\)

Write Empirical Formula

The empirical formula is based on the whole number ratio of elements. Hence, the empirical formula for uraninite is \(U_3O_8\).

Key concepts

Uraninite

Uraninite is a fascinating mineral primarily used for uranium extraction, crucial for nuclear energy. This mineral is predominantly composed of uranium oxides, which are compounds containing uranium and oxygen. Usually found in geological formations, it appears in various forms such as grainy or dense masses. Understanding the composition of uraninite is essential, particularly with its high uranium content. Uranium itself is a dense metal, known for its radioactive properties and its ability to sustain nuclear fission. Given its composition, uraninite is expressed in terms of mass percentages of uranium and oxygen. This mineral composition significantly influences its empirical formula, showing the simplest whole number ratio of the elements present.

Moles Calculation

The calculation of moles is a fundamental concept in chemistry, helping to understand the amount of a substance. In the context of uraninite, we start with a known sample mass. For simplicity, consider a sample mass of 100 grams. From there, derive the masses of uranium and oxygen based on the given percentages: - Uranium: 84.80 g out of 100 g sample - Oxygen: 15.20 g out of 100 g sample Next, use the molar masses to calculate the moles:

• The molar mass of uranium (U) is about 238 g/mol.
• The molar mass of oxygen (O) is about 16 g/mol.

Calculating the moles: - Moles of Uranium: Divide the mass of uranium by its molar mass, which equals approximately 0.356 mol. - Moles of Oxygen: Divide the mass of oxygen by its molar mass, which equals 0.950 mol. These calculations form the basis for determining the empirical formula, as they establish the ratio of elements.

Mass Percentage

Mass percentage is a way to express the concentration of an element in a compound. It is an essential concept in determining the composition of minerals like uraninite. To find mass percentage, divide the mass of a particular element by the total mass of the sample and multiply by 100: - In uraninite, uranium makes up 84.80% of the mass, meaning that, in a 100 g sample, 84.80 g is uranium. - Consequently, oxygen makes up the remaining 15.20%. By understanding these percentages, chemists can verify the compound's empirical formula by ensuring the resulting mole ratios reflect these given mass percentages. Such calculations substantiate the mineral's composition and guide further analysis.