A chemist wants to extract the gold from 15.0g of gold(II) chloride dihydrate, AuCl3 x 2H20, What mass of gold could be obtained from this sample?
Also how would you find the molar mass of of 2H20 with the coefficient 2 in front?
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The coefficient of 2 means to multiply by 2; the molar mass of H2O is 18, the molar mass of 2H2O is 36.
To find the mass of gold that could be obtained from the given sample, we need to determine the molar mass of the gold(II) chloride dihydrate (AuCl3 x 2H2O) and then calculate the mass of gold present in it.
Let's break down the steps to find the mass of gold:
Step 1: Find the molar mass of AuCl3 x 2H2O:
- The molar mass of gold (Au) = 196.97 g/mol (from the periodic table)
- The molar mass of chlorine (Cl) = 35.45 g/mol (from the periodic table)
- The molar mass of hydrogen (H) = 1.01 g/mol (from the periodic table)
- The molar mass of oxygen (O) = 16.00 g/mol (from the periodic table)
Using these values, we can calculate the molar mass of AuCl3 x 2H2O as follows:
Molar mass of AuCl3 x 2H2O = (196.97 g/mol) + (3 × 35.45 g/mol) + (2 × [(2 × 1.01 g/mol) + (1 × 16.00 g/mol)])
Simplifying the expression, we get:
Molar mass of AuCl3 x 2H2O = 196.97 g/mol + 106.35 g/mol + 36.04 g/mol
Molar mass of AuCl3 x 2H2O = 339.36 g/mol
So, the molar mass of AuCl3 x 2H2O is 339.36 g/mol.
Step 2: Calculate the mass of gold:
- We have 15.0g of AuCl3 x 2H2O.
- To calculate the mass of gold, we need to determine the proportion of gold in the compound.
The molar mass of gold is 196.97 g/mol. In 1 mole of AuCl3 x 2H2O, there is 1 mole of gold. Therefore, the proportion of gold in AuCl3 x 2H2O is:
(196.97 g/mol gold) / (339.36 g/mol AuCl3 x 2H2O)
Next, we can calculate the mass of gold as follows:
Mass of gold = Proportion of gold × Mass of AuCl3 x 2H2O
Mass of gold = (196.97 g/mol gold / 339.36 g/mol AuCl3 x 2H2O) × 15.0 g AuCl3 x 2H2O
Simplifying the expression, we get:
Mass of gold = 0.5807 × 15.0 g
Mass of gold = 8.71 g
Therefore, from 15.0 g of AuCl3 x 2H2O, a chemist could obtain approximately 8.71 g of gold.
Now let's address the second part of your question regarding the molar mass of 2H2O with a coefficient of 2 in front.
The formula 2H2O represents two water molecules, where each water molecule consists of two hydrogen atoms (H) and one oxygen atom (O).
- The molar mass of hydrogen (H) = 1.01 g/mol (from the periodic table)
- The molar mass of oxygen (O) = 16.00 g/mol (from the periodic table)
To find the molar mass of 2H2O, we multiply the molar mass of one water molecule (2H2O) by the coefficient 2.
Molar mass of 2H2O = 2 × (2 × 1.01 g/mol) + 16.00 g/mol
Simplifying the expression, we get:
Molar mass of 2H2O = 4.02 g/mol + 16.00 g/mol
Molar mass of 2H2O = 20.02 g/mol
Therefore, the molar mass of 2H2O with a coefficient of 2 in front is 20.02 g/mol.