A mercury mirror forms inside a test tube by the thermal decomposition of mercury(II) oxide.
2 HgO(s) 2 Hg(l) + O2(g)
Hrxn = 181.6 kJ
(a) How much heat is needed to decompose 556 g of the oxide?
(b) If 288 kJ of heat is absorbed, how many grams of mercury form?
bofa
(a) To calculate the amount of heat needed to decompose 556 g of the mercury(II) oxide, we can use the given enthalpy change of the reaction (ΔHrxn).
1 mole of HgO has a molar mass of 200.59 g.
So, 556 g of HgO is equal to (556 g / 200.59 g/mol) = 2.77 moles of HgO.
From the balanced equation, we can see that the molar ratio between HgO and ΔHrxn is 2:1.
Therefore, the amount of heat needed to decompose 2.77 moles of HgO is:
(2.77 moles HgO) x (181.6 kJ/1 mole HgO) = 502.29 kJ
Therefore, 502.29 kJ of heat is needed to decompose 556 g of the oxide.
(b) If 288 kJ of heat is absorbed, we can use the same molar ratio to calculate the amount of mercury formed.
From the balanced equation, the molar ratio between HgO and Hg is 2:2.
So, 181.6 kJ of heat is absorbed when 1 mole of HgO decomposes to form 1 mole of Hg.
To find the number of moles of Hg formed, we can use the ratio:
(288 kJ) x (1 mole HgO / 181.6 kJ) x (2 moles Hg / 2 moles HgO) = 1.583 moles Hg
The molar mass of Hg is 200.59 g/mol, so the mass of Hg formed is:
(1.583 moles Hg) x (200.59 g/mol) = 317.63 g
Therefore, 317.63 g of mercury would form if 288 kJ of heat is absorbed.
To answer these questions, we need to use the given information in the chemical equation and the concept of molar mass to calculate the values.
(a) To find out how much heat is needed to decompose 556 g of mercury(II) oxide, we can use the molar mass of HgO and the given enthalpy change:
1. Find the molar mass of HgO:
- Molar mass of Hg = 200.59 g/mol (from periodic table)
- Molar mass of O = 16.00 g/mol (from periodic table)
- Molar mass of HgO = (200.59 g/mol) + (16.00 g/mol) = 216.59 g/mol
2. Convert the given mass of HgO to moles:
- Moles of HgO = 556 g / 216.59 g/mol = 2.5674 mol
3. Use stoichiometry to determine the amount of heat required:
- From the balanced equation, the ratio of HgO to Hg is 2:2.
- Therefore, the moles of Hg produced will be the same as the moles of HgO consumed.
- So, the heat required to decompose 556 g of HgO is 2.5674 mol × 181.6 kJ/mol = 466.2 kJ.
Therefore, the amount of heat needed to decompose 556 g of mercury(II) oxide is 466.2 kJ.
(b) To calculate the number of grams of mercury formed when 288 kJ of heat is absorbed, we can use the molar mass of Hg and the given enthalpy change:
1. From the balanced equation, the ratio of HgO to Hg is 2:2.
2. Since the enthalpy change is positive in this case, it means that heat is absorbed to decompose the HgO.
3. Use stoichiometry to determine the moles of Hg formed:
- Moles of Hg = (288 kJ / 181.6 kJ/mol) × 2 mol = 3.9896 mol
4. Convert moles of Hg to grams:
- Mass of Hg = 3.9896 mol × 200.59 g/mol = 801.29 g
Therefore, when 288 kJ of heat is absorbed, approximately 801.29 grams of mercury will form.