Consider an alloy that is 13.4% copper by mass in tin. Copper makes up what percentage of the atoms in this sample?
100% * [13.4 / (atomic mass Cu)] /
... {[13.4 / (atomic mass Cu)] + [(100 - 13.4) / (atomic mass Sn)]}
To determine the percentage of copper atoms in the alloy, we need to know the molar masses of copper and tin.
The molar mass of copper (Cu) is 63.55 g/mol, and the molar mass of tin (Sn) is 118.71 g/mol.
First, we need to find the number of moles of copper in the alloy.
Assume we have 100 g of this alloy. This means we have:
13.4 g of copper (13.4% of 100 g)
86.6 g of tin (100 g - 13.4 g)
Next, we calculate the number of moles of each element:
Number of moles of copper = mass of copper / molar mass of copper
Number of moles of copper = 13.4 g / 63.55 g/mol ≈ 0.2110 mol
Number of moles of tin = mass of tin / molar mass of tin
Number of moles of tin = 86.6 g / 118.71 g/mol ≈ 0.7294 mol
Now, we need to find the ratio of the moles of copper to the total moles:
Percentage of copper atoms = (moles of copper / total moles) × 100%
Percentage of copper atoms = (0.2110 mol / (0.2110 mol + 0.7294 mol)) × 100%
Percentage of copper atoms ≈ 22.4%
Therefore, copper makes up approximately 22.4% of the atoms in this alloy.
To determine the percentage of copper atoms in the alloy, we need to make use of the concept of molar mass and atomic mass of copper and tin.
First, we need to find the molar mass of copper (Cu) and tin (Sn). The atomic masses of copper and tin are approximately 63.55 g/mol and 118.71 g/mol, respectively.
Next, we can calculate the molar mass of the alloy using the mass percentages of copper and tin. Assuming we have 100 grams of the alloy, the mass of copper would be 13.4 grams and the mass of tin would be 100 - 13.4 = 86.6 grams.
Now, to find the moles of copper and tin present in the alloy, we divide the mass values by their respective molar masses:
Moles of copper = Mass of copper / Molar mass of copper
Moles of copper = 13.4 g / 63.55 g/mol
Moles of tin = Mass of tin / Molar mass of tin
Moles of tin = 86.6 g / 118.71 g/mol
Next, we need to determine the ratio of copper atoms to tin atoms in the alloy. This can be done by dividing the moles of copper and tin by the smallest number of moles:
Ratio = Moles of copper / Moles of tin
Finally, to find the percentage of copper atoms in the alloy, we multiply the ratio by 100:
Percentage of copper atoms = Ratio × 100
By following these steps and plugging in the values, you can calculate the percentage of copper atoms in the alloy.