Copper (Cu) reacts with sulfer (S) to form copper sulfide as shown in the equation. A scientist adds 12.7 grams of Cu to 3.2 grams of S to start the reaction. In this reaction, all of the copper and all of the sulfur react. Before running the experiment, the scientist expected the products of the reaction will be a total of 15.9 grams of copper sulfide (Cu2S).
To determine if the scientist's expectations are correct, we need to calculate the theoretical yield of copper sulfide based on the given amounts of copper and sulfur.
First, we need to find the molar mass of copper (Cu) and sulfur (S). The molar mass of Cu is 63.55 g/mol, and the molar mass of S is 32.06 g/mol.
Next, we calculate the number of moles of Cu and S in the given amounts:
Number of moles of Cu = mass of Cu / molar mass of Cu = 12.7 g / 63.55 g/mol = 0.2 mol
Number of moles of S = mass of S / molar mass of S = 3.2 g / 32.06 g/mol = 0.1 mol
According to the balanced equation, the molar ratio of Cu to Cu2S is 1:1. Therefore, the number of moles of Cu2S formed will be equal to the number of moles of Cu reacted.
Number of moles of Cu2S formed = 0.2 mol
Finally, we calculate the mass of Cu2S formed using the molar mass of Cu2S:
Mass of Cu2S formed = number of moles of Cu2S formed x molar mass of Cu2S
= 0.2 mol x (2 x (63.55 g/mol) + 32.06 g/mol)
= 0.2 mol x 159.16 g/mol
= 31.832 g
Based on the calculations, the theoretical yield of copper sulfide (Cu2S) is 31.832 grams. This is greater than the expected yield of 15.9 grams, so it is likely that the scientist's expectations were incorrect.
To solve this problem, we can use the concept of stoichiometry to determine the mass of the copper sulfide (Cu2S) formed.
First, let's write down the balanced equation for the reaction:
Cu + S -> Cu2S
According to the equation, 1 mole of Cu reacts with 1 mole of S to form 1 mole of Cu2S.
Step 1: Calculate the number of moles of Cu and S
- The molar mass of Cu is 63.55 g/mol.
- The molar mass of S is 32.07 g/mol.
- Using the given masses, we can calculate the number of moles:
moles of Cu = mass of Cu / molar mass of Cu
moles of Cu = 12.7 g / 63.55 g/mol
moles of Cu = 0.2 mol
moles of S = mass of S / molar mass of S
moles of S = 3.2 g / 32.07 g/mol
moles of S = 0.1 mol
Step 2: Determine the limiting reactant
Since we have 0.2 moles of Cu and 0.1 moles of S, Cu is in excess because we have twice the moles required for the reaction.
Step 3: Calculate the theoretical yield of Cu2S.
The balanced equation shows that 1 mole of Cu reacts to form 1 mole of Cu2S. Therefore, we expect the same number of moles of Cu2S as we have moles of Cu.
moles of Cu2S = moles of Cu = 0.2 mol
Step 4: Calculate the mass of Cu2S
To find the mass of Cu2S, we can use the molar mass of Cu2S, which is 159.17 g/mol.
mass of Cu2S = moles of Cu2S * molar mass of Cu2S
mass of Cu2S = 0.2 mol * 159.17 g/mol
mass of Cu2S = 31.83 g
Step 5: Compare the actual yield to the expected yield
The scientist expected 15.9 grams of Cu2S, but the actual yield is 31.83 grams. Therefore, the actual yield is greater than the expected yield.
Note: It's important to note that the given masses in the problem may not be accurate or include impurities that could affect the yield.
To determine whether the expected mass of the product matches the actual mass, we can calculate the theoretical yield of copper sulfide based on the balanced chemical equation and then compare it to the expected mass.
First, we need to write the balanced chemical equation for the reaction between copper (Cu) and sulfur (S):
Cu + S → Cu2S
According to the equation, 1 mole of copper reacts with 1 mole of sulfur to produce 1 mole of copper sulfide (Cu2S).
We can calculate the molar masses to convert grams to moles:
Molar mass of Cu = 63.55 g/mol
Molar mass of S = 32.06 g/mol
Molar mass of Cu2S = (2 x 63.55 g/mol) + 32.06 g/mol = 159.16 g/mol
Using the molar masses, we can convert the masses of Cu and S to moles:
Moles of Cu = 12.7 g / 63.55 g/mol = 0.20 mol
Moles of S = 3.2 g / 32.06 g/mol = 0.10 mol
Since the balanced equation shows a 1:1 ratio of Cu to S, we can determine the limiting reactant. In this case, sulfur (S) is the limiting reactant because there are fewer moles of it compared to copper (Cu).
Therefore, all 0.10 moles of sulfur will react with 0.10 moles of copper to form copper sulfide (Cu2S).
To calculate the theoretical yield of copper sulfide, we can use the molar ratio between Cu2S and S:
Moles of Cu2S = 0.10 mol
Now, we can convert moles of Cu2S to grams using its molar mass:
Mass of Cu2S = 0.10 mol x 159.16 g/mol = 15.92 g
The theoretical yield of copper sulfide is calculated to be 15.92 grams.
Comparing the expected mass (15.9 grams) to the theoretical yield (15.92 grams), we can see that they are very close. Therefore, the expected mass of 15.9 grams of copper sulfide matches the actual mass based on the balanced equation and stoichiometry calculations.