ChemTeam: Determine identity of an element from a binary formula and mass data - Problems #1

Determine identity of an element from a binary formula and mass data
Problems #1 - 10

Problem #1: An unknown metal M reacts with oxygen to give the metal oxide MO₂. Identify the metal based on the following information.

mass of metal: 0.356 g
mass of metal oxide: 0.452 g

Solution:

1) Mass of the oxygen in MO₂:

0.452 − 0.356 = 0.096 g

2) Moles of oxygen in MO₂:

0.096 g / 16.00 g/mol = 0.0060 mol

3) The moles of M in the sample of MO₂:

the molar ratio of M and O in the formula is 1 to 2
1 is to 2 as x is to 0.0060
x = 0.0030 mol

4) Calculate atomic weight and identify M:

0.356 g / 0.0030 mol = 118.7 g/mol
Tin

Problem #2: 16.5 g of element X reacts completely with 9.6 g of oxygen to produce a pure sample of XO₂. Find the atomic weight and identity of X.

Solution:

9.6 g / 16.00 g/mol = 0.60 mol
mole ratio of X and O in the formula is 1 to 2. Therefore:
1 is to 2 as x is to 0.60
x = 0.30 mol (this is moles of X in the 26.1 g of XO₂)
16.5 g / 0.30 mol = 55 g/mol
Manganese

Problem #3: An element reacts with bromine to give the bromide, MBr₅. If 2.009 g of the element gives 10.648 g of MBr₅, what is the element?

Solution:

1) How much Br is present in the sample?

10.648 − 2.009 = 8.639 g

2) How many moles is this?

8.639 g / 79.904 g/mol = 0.108117 mol

3) From the formula, we know that M and Br are in a 1 to 5 molar ratio. We use a ratio and proportion to get the moles of M.

1 is to 5 as x is to 0.108117
x = 0.0216234 mol

4) We now know a mass of M and how many moles that mass is. To get the molar mass of M, we do this:

2.009 g / 0.0216234 mol = 92.9 g/mol
Niobium

Problem #4: A student places 5.00 g of an unknown metal (X) ribbon in a crucible. The crucible is heated until the unknown metal reacted with oxygen to form a white product with the formula X₂O₃ . The mass of product is determined to be 7.19 g.

(a) What is the molar mass of the unknown metal (X)?
(b) What element is the unknown metal?

Solution:

1) Mass of oxygen:

7.19 − 5.00 = 2.19 g

2) Moles of oxygen:

2.19 g / 16.00 g/mol = 0.136875 mol

3) Use ratio and proportion to determine moles of X:

2 is to 3 as y is to 0.136875
y = 0.09125 mol

4) Determine molar mass of X:

5.00 g / 0.09125 mol = 54.8 g/mol
Manganese

Problem #5: A 30.6-g sample of the compound M₂O₃ contains 9.79 g of oxygen atoms. What is the molar mass of element M? Identify the element M most probably is.

Solution:

1) Set up the following ratio and proportion:

30.6 9.79
–––––– = ––––
2x + 48 48

9.79 g / 48 g ---> The moles of O in 30.6 g of M₂O₃
48 g ---> There are 48 g in three moles of oxygen. The three comes from oxygen's subscript in the formula. (I suppose I should write 48 g/3mol.
2x + 48 ---> The molar mas of M₂O₃. x is the atomic weight of M, note that is multiplied by two because of the subscripted two in the formula.

2) Cross multiply and divide:

(9.79) (2x + 48) = (48) (30.6)
(9.79) (2x + 48) = 1468.8
2x + 48 = 150
2x = 102
x = 51 g/mol
Vanadium

Problem #6: From a specific heat measurement, the approximate atomic weight of a metal (M) is found to be 135 Daltons. A 0.2341 g sample of M is heated to constant weight in air to convert it to the oxide The weight of the residue is 0 2745 g. Find the true atomic weight of the metal (and therefore its identity), and determine the formula of the metal oxide.

Solution:

1) Determine the moles of M and O present:

M ---> 2341 g / 135 g/mol = 17.34 mol
O ---> 404 g / 16.0 g/mol = 25.25 mol

2) Determine lowest whole-number ratio:

M ---> 17.34 mol / 17.34 mol = 1
O ---> 25.25 mol /17.34 mol = 1.456
3) This yields a ratio of 2 to 2.9 leading to the conclusion that the empirical formula is M₂O₃.
4) Note that I scaled the weight values to 2341 g and 2745 g. I did this for convenience. Also, the 404 comes from 2745 minus 2341.

5) Determine the percent composition of M in M₂O₃:

2341 g / 2745 g = 0.8528 (leave it as a decimal value)

6) The calculation for the percent composition of M in M₂O₃ is this:

2X
––––––– = 0.8528
2X + 48

Where X is the atomic weight of M and 48 is the weight of three O.

7) Solve for X:

2X = 1.7056X + 40.9344
0.2944X = 40.9344
X = 139

8) This experiment yields lanthanum as the most probable answer. Since our starting data was approximate, more tests would be required. For example, Ba is a possibility, but Ba forms BaO when heated in air. In like fashion, Cs can be excluded based in its formation of Cs₂O. However, Ce₂O₃ can form, therefore, if this was a real-world situation, additional tests would be performed to distinguish between La and Ce.

Problem #7: Identify M in the compound M₂(C₂O₄)₃ if the mass of the M atoms is 1371 g in a sample containing 5.92 x 10²⁴ molecules of M₂(C₂O₄)₃

Solution:

5.92 x 10²⁴ molecules of M₂(C₂O₄)₃ contain 2 x 5.92 x 10²⁴ = 1.184 x 10²⁵ atoms of M
Moles of M = (1.184 x 10²⁵ atoms) / (6.022 x 10²³ atoms/mol) = 19.66 mol
Molar mass = 1371 g / 19.66 mol = 69.74 g/mol
Gallium (molar mass of 69.723 g/mol) is the most reasonable answer.

Problem #8: If 3.72 g of element X exactly reacts with 4.80 g of oxygen to form a compound whose molecular formula is shown, from other experiments to be X₄O₁₀, what is the relative atomic mass of X? What element is X?

Solution:

1) Let's assume "4.80 g of oxygen" means O:

(4.80 grams O) (1 mol O / 16.0 g O) = 0.30 mol of O
(0.30 mol O) (4 mol X / 10 mol O) = 0.12 mol X
3.72 g X / 0.12 mol X = 31.0 g/mol
phosphorous

2) Let's assume "4.80 g of oxygen" means O₂:

(4.80 grams O₂) (1 mol O₂ / 32.0 g O₂) (2 mol O / 1 mol O₂) = 0.30 mol of O
(0.30 mol O) (4 mol X / 10 mol O) = 0.12 mol X
3.72 g X / 0.12 mol X = 31.0 g/mol
phosphorous

Problem #9: Determine the atomic weight of element A, given that 8.00 g of A₂O₃ contains 2.40 g of oxygen.

Solution:

1) Determine moles of oxygen:

2.40 g / 16.0 g/mol = 0.15 mol

2) Determine moles of A:

2 is to 3 as x is to 0.15
x = 0.10 mol

3) Determine atomic weight of A:

8.00 g − 2.40 g = 5.60 g
5.60 g / 0.10 mol = 56 g/mol
Although not asked for, element A is most likely iron.

Problem #10: A 2.00 g sample of a metal X (that is known to form X²⁺ ions) was added to 0.100 L of 0.500 M H₂SO₄. After all the metal had reacted, the remaining acid required 0.0637 L of 0.500 M NaOH solution for neutralization. Calculate the atomic weight of the metal and identify the element.

Solution:

1) Determine moles NaOH: