how many grams of pure uranium can theoretically be extracted from 10.0kg sample of pitchblende which is 92.0%uo2
To determine how many grams of pure uranium (U) can be extracted from a sample of pitchblende containing 92.0% UO2, we need to follow these steps:
Step 1: Calculate the mass of UO2 in the sample:
- The mass of the UO2 can be found by multiplying the mass of the sample by its concentration of UO2.
mass of UO2 = mass of sample × concentration of UO2
mass of UO2 = 10.0 kg × 0.920
mass of UO2 = 9.20 kg
Step 2: Calculate the molar mass of UO2:
- The molar mass of UO2 can be determined by adding the atomic masses of uranium (U) and oxygen (O).
molar mass of UO2 = atomic mass of U + 2 × atomic mass of O
molar mass of UO2 = 238.03 g/mol + 2 × 16.00 g/mol
molar mass of UO2 = 270.03 g/mol
Step 3: Determine the number of moles of UO2:
- The number of moles of UO2 can be calculated by dividing its mass by its molar mass.
moles of UO2 = mass of UO2 / molar mass of UO2
moles of UO2 = 9.20 kg / 270.03 g/mol
moles of UO2 = 34.06 mol
Step 4: Calculate the number of moles of U:
- Since one mole of UO2 contains one mole of uranium (U), the number of moles of U will be the same as the moles of UO2.
moles of U = moles of UO2
moles of U = 34.06 mol
Step 5: Convert moles of U to grams:
- The mass of U can be obtained by multiplying the number of moles by its molar mass.
mass of U = moles of U × molar mass of U
mass of U = 34.06 mol × 238.03 g/mol
mass of U = 8107.32 g
Therefore, theoretically, approximately 8107.32 grams of pure uranium can be extracted from a 10.0 kg sample of pitchblende containing 92.0% UO2.
To calculate the amount of pure uranium that can be extracted from the 10.0 kg sample of pitchblende, you need to multiply the mass of the sample by the percentage of uranium present in the compound.
Given that the pitchblende sample is 92.0% UO2, it means that 92.0% of the sample's mass is uranium.
First, convert the percentage to a decimal by dividing it by 100:
92.0% = 92.0/100 = 0.92
Next, multiply the mass of the sample by the decimal value obtained:
Pure uranium mass = 10.0 kg * 0.92 = 9.2 kg
To convert the mass from kilograms to grams, simply multiply by 1000:
Pure uranium mass = 9.2 kg * 1000 = 9200 grams
Therefore, theoretically, 9200 grams of pure uranium can be extracted from the 10.0 kg sample of pitchblende.