Determine the percent composition of chromium in chromium(II) dichromate.
The correct answer and explanation is:
To determine the percent composition of chromium (Cr) in chromium(II) dichromate, we must:
Step 1: Determine the chemical formula
Chromium(II) = Cr²⁺
Dichromate = Cr₂O₇²⁻
To balance charges:
1 Cr²⁺ ion balances with 1 Cr₂O₇²⁻ ion
So the formula is: Cr(Cr₂O₇)
Step 2: Determine the molar mass of Cr(Cr₂O₇)
Break it down:
- Chromium (Cr): 3 atoms
Atomic mass ≈ 51.996 g/mol
→ 3 × 51.996 = 155.988 g/mol - Oxygen (O): 7 atoms
Atomic mass ≈ 16.00 g/mol
→ 7 × 16.00 = 112.00 g/mol
Total molar mass = 155.988 + 112.00 = 267.988 g/mol
Step 3: Calculate the percent composition of chromium
Percent Cr=(Mass of CrMolar Mass of Cr(Cr2O7))×100\text{Percent Cr} = \left( \frac{\text{Mass of Cr}}{\text{Molar Mass of Cr(Cr}_2\text{O}_7)} \right) \times 100 =(155.988267.988)×100≈58.22%= \left( \frac{155.988}{267.988} \right) \times 100 \approx \boxed{58.22\%}
Explanation (Approx. 300 words):
Percent composition tells us what portion (by mass) of a compound is made up of a specific element. In this case, we are asked to find the percent composition of chromium in chromium(II) dichromate.
First, we identify the chemical formula. Chromium(II) means the chromium ion has a +2 charge (Cr²⁺), and dichromate is a polyatomic ion with the formula Cr₂O₇²⁻. To create a neutral compound, one Cr²⁺ ion must pair with one Cr₂O₇²⁻ ion, since their charges cancel out. This gives the formula Cr(Cr₂O₇). This compound contains 3 chromium atoms—one from Cr²⁺ and two from Cr₂O₇²⁻.
Next, we calculate the molar mass (the mass of one mole of the compound). Each chromium atom has an atomic mass of about 51.996 g/mol, and there are three chromium atoms total, so their combined mass is about 155.988 g/mol. There are 7 oxygen atoms in Cr₂O₇, each about 16.00 g/mol, so the oxygen total is 112.00 g/mol. Together, the molar mass of the compound is 267.988 g/mol.
Finally, to find the percent composition of chromium, we divide the mass of chromium (155.988 g/mol) by the total molar mass (267.988 g/mol) and multiply by 100. The result is 58.22%, meaning chromium makes up about 58.22% of the mass of chromium(II) dichromate.