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.
To determine the mass of gold that can be extracted, we need to use stoichiometry and the balanced chemical equation. The balanced equation shows the ratio of moles between the substances involved. Here are the steps to calculate the mass of gold that can be extracted:
Step 1: Calculate the molar mass of sodium cyanide (NaCN).
The molar mass of NaCN can be calculated by adding the atomic masses of each element in the compound.
Molar mass of NaCN = (sodium atomic mass) + (carbon atomic mass) + (nitrogen atomic mass)
= (22.99 g/mol) + (12.01 g/mol) + (14.01 g/mol)
= 49.01 g/mol
Step 2: Convert the given mass of sodium cyanide to moles.
To convert mass to moles, use the formula:
moles = mass / molar mass
moles of NaCN = 27.4 g / 49.01 g/mol
= 0.559 mol
Step 3: Determine the stoichiometric ratio between NaCN and Au.
According to the balanced equation, the stoichiometric ratio is 8:4. This means that for every 8 moles of NaCN, 4 moles of gold can be extracted.
Step 4: Calculate the moles of gold that can be extracted.
moles of Au = (moles of NaCN) × (4 moles of Au / 8 moles of NaCN)
= 0.559 mol × (4/8)
= 0.28 mol
Step 5: Convert the moles of gold to mass.
mass of Au = (moles of Au) × (molar mass of Au)
= 0.28 mol × (197 g/mol)
= 55.16 g
Therefore, the mass of gold that can be extracted using 27.4 g sodium cyanide is approximately 55.16 grams.