To extract gold from its ore, the ore is treated with sodium cyanide solution in the presence of oxygen and water.
4 Au(s) + 8 NaCN(aq) + O2(g) + 2 H2O(l) 4 NaAu(CN)2(aq) + 4 NaOH(aq)
(a) Determine the mass of gold that can be extracted if 29.3 g sodium cyanide is used.
(b) If the mass of the ore from which the gold was extracted is 146.5 g, what percentage of the ore is gold?
To calculate the mass of gold extracted and the percentage of gold in the ore, we need to use the given balanced chemical equation and apply stoichiometry.
(a) Determine the mass of gold that can be extracted if 29.3 g of sodium cyanide is used.
To find the mass of gold, we need to determine the mole ratio between sodium cyanide and gold in the balanced chemical equation.
From the balanced equation, we can see that 4 moles of gold (Au) react with 8 moles of sodium cyanide (NaCN). Therefore, the mole ratio is:
4 moles Au / 8 moles NaCN.
We can calculate the molar mass of sodium cyanide (NaCN) to convert the given mass of sodium cyanide to moles.
Na - 22.99 g/mol
C - 12.01 g/mol
N - 14.01 g/mol
Molar mass of NaCN = 22.99 g/mol + 12.01 g/mol + 14.01 g/mol = 49.02 g/mol
Now, we can calculate the number of moles of sodium cyanide:
Number of moles = Mass / Molar mass
Number of moles NaCN = 29.3 g / 49.02 g/mol = 0.598 mol
Using the mole ratio from the balanced equation, we can determine the moles of gold that can be extracted:
Moles of gold = (Number of moles NaCN) × (4 moles Au / 8 moles NaCN)
Moles of gold = 0.598 mol × (4/8) = 0.299 mol
Finally, we can convert moles of gold to mass:
Mass of gold = Moles of gold × Molar mass Au
The molar mass of gold (Au) is 196.97 g/mol.
Mass of gold = 0.299 mol × 196.97 g/mol = 59.02 g
Therefore, the mass of gold that can be extracted is 59.02 g when 29.3 g of sodium cyanide is used.
(b) If the mass of the ore from which the gold was extracted is 146.5 g, what percentage of the ore is gold?
To find the percentage of gold in the ore, we can use the mass of gold calculated in part (a) and the mass of the ore.
Percentage of gold = (Mass of gold / Mass of ore) × 100
Percentage of gold = (59.02 g / 146.5 g) × 100 = 40.29%
Therefore, approximately 40.29% of the ore is gold.