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)
Determine the mass of gold that can be extracted if 27.4 g sodium cyanide is used.
If the mass of the ore from which the gold was extracted is 157.0 g, what percentage of the ore is gold?
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To determine the mass of gold that can be extracted, we need to use stoichiometry. Stoichiometry is a branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions.
Step 1: Balance the equation
We already have a balanced equation above.
Step 2: Calculate the molar mass of sodium cyanide (NaCN)
The molar mass of NaCN is determined by adding up the atomic masses of its constituent elements:
Na: 22.99 g/mol
C: 12.01 g/mol
N: 14.01 g/mol
Adding them up gives us: 22.99 + 12.01 + 14.01 = 49.01 g/mol
Step 3: Calculate the moles of sodium cyanide used
To convert mass to moles, we need to use the formula:
moles = mass / molar mass
Given that the mass of sodium cyanide used is 27.4 g, we can calculate the moles as follows:
moles = 27.4 g / 49.01 g/mol = 0.559 mol
Step 4: Use the stoichiometry of the balanced equation to determine the moles of gold extracted
From the balanced equation, we can see that the molar ratio between NaCN and Au is 8:4.
Therefore, for every 8 moles of NaCN used, 4 moles of Au are extracted.
Using this ratio, we can determine the moles of gold extracted:
moles of Au = (moles of NaCN) x (4 moles of Au / 8 moles of NaCN) = 0.559 mol x 4/8 = 0.2795 mol
Step 5: Calculate the mass of gold extracted
To calculate the mass of gold extracted, we use the formula:
mass = moles x molar mass
Since the molar mass of gold (Au) is 196.97 g/mol, we can calculate the mass of gold extracted as follows:
mass = 0.2795 mol x 196.97 g/mol = 55.08 g
Therefore, 55.08 grams of gold can be extracted when 27.4 grams of sodium cyanide is used.
To calculate the percentage of gold in the ore, we need to use the given mass of the ore.
Given that the mass of the ore is 157.0 g and the mass of gold extracted is 55.08 g, we can calculate the percentage of gold in the ore using the formula:
percentage of gold = (mass of gold extracted / mass of ore) x 100
percentage of gold = (55.08 g / 157.0 g) x 100 = 35.05%
Therefore, the percentage of gold in the ore is approximately 35.05%.