Uranium is used as a fuel, primarily in the form of uranium(IV) oxide, in nuclear power plants. A small
sample of uranium metal (0.169 g) is heated to between 800 and 900 0C in air to give 0.199 g of a dark
green oxide, UxOy. (a) How many moles of uranium metal were used? (b) What is the empirical formula of
the oxide, UxOy?
mols U metal = grams/atomic mass = 0.169/238 = 0.00071
U + O2 ==> UxOy
mass O is UxOy = mass UxOy - mass U = 0.199 - 0.169 = 0.030 g
mols U metal from above = 0.000710
mol O = 0.030/16 = 0.00187
Now you want to find the mole ratio. The easy way to do this is to divide both numbers of the smaller number; i.e.,
mols U = 0.000710/0.000710 = 1.000
mols O = 0.00187/0.000710 = 2.63
Compounds don't have ratios that are not whole numbers so multiply by whole numbers until we find BOTH whole numbers. Multiply by 2 gives
U = 1.000 x 2 = 2.000
O = 2.634 x 2 = 5.27. Doesn't work so try 3.
U = 1.000 x 3 = 3.000
O = 2.634 x 3 = 7.902 which is close enough to round to 8 so the empirical formula is U3O8
To find the answers to these questions, we'll follow a step-by-step approach. Let's start by answering part (a).
(a) How many moles of uranium metal were used?
To calculate the number of moles of uranium metal (U) in the sample, we'll use the molar mass of uranium. The molar mass of uranium is 238.03 g/mol.
Step 1: Convert the mass of uranium metal from grams to moles.
Given:
Mass of uranium metal (m) = 0.169 g
Molar mass of uranium (M) = 238.03 g/mol
Number of moles (n) = mass (m) / molar mass (M)
n = 0.169 g / 238.03 g/mol
n ≈ 0.00071 mol
Therefore, approximately 0.00071 moles of uranium metal were used.
Now, let's proceed to answer part (b) and determine the empirical formula of the oxide, UxOy.
(b) What is the empirical formula of the oxide, UxOy?
To find the empirical formula, we need to compare the moles of uranium and oxygen in the given sample.
Step 1: Calculate the moles of oxygen in the oxide.
Given:
Mass of the green oxide (m_oxide) = 0.199 g
Total moles of uranium (n_uranium) = 0.00071 mol
To find the moles of oxygen, we need to subtract the moles of uranium from the total moles of the oxide.
Moles of oxygen (n_oxygen) = Total moles of the oxide - Moles of uranium
n_oxygen = m_oxide / molar mass of the oxide - n_uranium
Since the molar mass of the oxide is not given, we need to calculate it.
Step 2: Calculate the molar mass of the oxide.
Given:
Mass of the green oxide (m_oxide) = 0.199 g
To calculate the molar mass of the oxide, we need to know its formula. Let's assume it is UxOy.
Molar mass of the oxide (M_oxide) = (Molar mass of uranium (M_uranium) x x) + (Molar mass of oxygen (M_oxygen) x y)
To find the empirical formula, we can assume that the smallest whole-number ratio of atoms corresponds to x = 1 and y = 1. This means that the empirical formula is U1O1 or simply UO.
Therefore, the empirical formula of the oxide is UO.
To summarize:
(a) Approximately 0.00071 moles of uranium metal were used.
(b) The empirical formula of the oxide is UO.