14 carat gold has a purity of 58.3%. How
many moles of gold are in 137 grams of 14
carat gold?
Answer in units of moles.
137 g 14K Au x 0.583 = g pure Au.
moles = grams/molar mass.
To find the number of moles of gold in 137 grams of 14 carat gold, we first need to calculate the mass of pure gold in 137 grams of 14 carat gold.
The purity of 14 carat gold is 58.3%, which means that 100 grams of 14 carat gold contains 58.3 grams of pure gold.
To calculate the mass of pure gold in 137 grams of 14 carat gold, we can set up a proportion:
(58.3 grams of pure gold / 100 grams of 14 carat gold) = (x grams of pure gold / 137 grams of 14 carat gold)
Cross multiplying the proportion, we get:
58.3 grams of pure gold * 137 grams of 14 carat gold = 100 grams of 14 carat gold * x grams of pure gold
Simplifying the equation:
x = (58.3 * 137) / 100
x = 79.771 grams of pure gold
Now, we need to convert the mass of pure gold from grams to moles. The molar mass of gold is approximately 197 grams/mol.
To calculate the number of moles of gold, we can use the formula:
moles = mass / molar mass
moles = 79.771 grams / 197 grams/mol
Simplifying the equation:
moles = 0.405 moles
Therefore, there are approximately 0.405 moles of gold in 137 grams of 14 carat gold.
To calculate the number of moles of gold in 137 grams of 14-carat gold, we need to use the molar mass of gold and the given purity.
First, we need to know the molar mass of gold. The molar mass of an element is the mass of one mole of atoms of that element. The atomic mass of gold (Au) is approximately 197 grams/mole.
Next, we need to calculate the mass of pure gold in the given 137 grams of 14-carat gold.
Since 14-carat gold has a purity of 58.3%, it means that 58.3% of the 137 grams is pure gold. We can calculate this as:
Mass of pure gold = 0.583 * 137 grams
Now, we can use the molar mass of gold to convert the mass of pure gold to moles:
Number of moles of gold = (Mass of pure gold) / (Molar mass of gold)
Plugging in the values, we have:
Number of moles of gold = (0.583 * 137 grams) / (197 grams/mole)
Simplifying the expression:
Number of moles of gold = 80.071 grams / 197 grams/mole
Calculating the value:
Number of moles of gold ≈ 0.406 moles
So, there are approximately 0.406 moles of gold in 137 grams of 14-carat gold.