If a 0.192 g sample of copper metal reacts with elemental sulfur to form 0.240 g of the sulfide product, (a) find the percent by mass of copper and sulfur in the product and (b) find the empirical formula of the copper sulfide

0.240g = mss Cu + S compound

-0.192g = mass Cu
---------------
0.048 g = S added to the Cu

%Cu = (mass Cu/mass total)*100 = ?

Take a 100 g sample.
mols Cu = grams/atomic mass Cu
mols S = grams/atomic mass S

Find the ratio of Cu to S with the smaller number being 1.00
Post your work if you get stuck.
%S = (mass S/mass total)*100 = ?

Well, well, well. It seems like copper and sulfur decided to have a little party and make some sulfide product. Let's do some math and find out what the party was all about!

(a) To find the percent by mass of copper and sulfur in the product, we need to compare the masses of each element to the total mass of the product. So, let's do some simple calculations.

Mass of copper = 0.240 g - 0.192 g = 0.048 g
Mass of sulfur = 0.240 g - 0.048 g = 0.192 g

Now, let's find the percent by mass for each element:
Percent copper = (mass of copper / total mass of product) x 100%
Percent copper = (0.048 g / 0.240 g) x 100% ≈ 20%

Percent sulfur = (mass of sulfur / total mass of product) x 100%
Percent sulfur = (0.192 g / 0.240 g) x 100% ≈ 80%

So, the percent by mass of copper in the product is approximately 20%, while the percent by mass of sulfur is approximately 80%. Looks like the sulfur had a blast at the party!

(b) Now, let's find the empirical formula of the copper sulfide. The empirical formula tells us the simplest whole-number ratio of the elements in a compound. To find it, we need to convert the mass of each element to moles and then divide by the smallest number of moles.

First, let's find the number of moles of copper:
Number of moles of copper = mass of copper / molar mass of copper
Number of moles of copper = 0.048 g / 63.55 g/mol ≈ 0.000756 mol

Next, let's find the number of moles of sulfur:
Number of moles of sulfur = mass of sulfur / molar mass of sulfur
Number of moles of sulfur = 0.192 g / 32.07 g/mol ≈ 0.00599 mol

To get the simplest whole-number ratio, we divide the number of moles of each element by the smallest number of moles, which is 0.000756 mol. So, we have:

0.000756 mol copper / 0.000756 mol ≈ 1
0.00599 mol sulfur / 0.000756 mol ≈ 7.92

And there you have it, my dear inquisitive friend! The empirical formula of the copper sulfide is approximately "CuS8". Quite an enthusiastic bunch, aren't they?

To find the percent by mass of copper and sulfur in the product, we need to calculate the masses of each element present.

(a) Finding the percent by mass of copper and sulfur in the product:

1. Calculate the mass of copper:

Mass of copper = Mass of product - Mass of sulfur
Mass of copper = 0.240 g - 0.192 g
Mass of copper = 0.048 g

2. Calculate the percent by mass of copper:

Percent by mass of copper = (Mass of copper / Mass of product) x 100
Percent by mass of copper = (0.048 g / 0.240 g) x 100
Percent by mass of copper = 20%

3. Calculate the percent by mass of sulfur:

Percent by mass of sulfur = ((Mass of sulfur) / (Mass of product)) x 100
Percent by mass of sulfur = ((0.192 g) / (0.240 g)) x 100
Percent by mass of sulfur = 80%

(b) Finding the empirical formula of the copper sulfide:

1. Convert the mass of copper and sulfur to moles using their molar masses. The molar masses are:

Copper (Cu) = 63.55 g/mol
Sulfur (S) = 32.06 g/mol

Moles of copper = Mass of copper / Molar mass of copper
Moles of copper = 0.048 g / 63.55 g/mol
Moles of copper = 0.00076 mol

Moles of sulfur = Mass of sulfur / Molar mass of sulfur
Moles of sulfur = 0.192 g / 32.06 g/mol
Moles of sulfur = 0.006 mol

2. Find the simplest ratio of moles by dividing each mole value by the smallest mole value:

Simplest ratio = (Moles of copper) / (Moles of sulfur)
Simplest ratio = 0.00076 mol / 0.006 mol
Simplest ratio = 0.1267

3. Round the ratio to the nearest whole number to obtain the subscripts for the empirical formula:

Empirical formula of copper sulfide = Cu₈S

Thus, the empirical formula of the copper sulfide compound is Cu₈S.

To find the percent by mass of copper and sulfur in the product, we need to use the given masses of copper and sulfur in the reaction.

(a) Percent by mass of copper:
First, we need to determine the mass of copper in the product. We know that the sample of copper metal reacted completely to form the copper sulfide product, so the mass of copper in the product is the same as the initial mass of copper.
Mass of copper in the product = 0.192 g

Next, we calculate the percent by mass of copper using the formula:
Percent by mass of copper = (mass of copper / mass of product) x 100%

Percent by mass of copper = (0.192 g / 0.240 g) x 100% = 80%

Therefore, the percent by mass of copper in the product is 80%.

To find the percent by mass of sulfur, we can use the same approach:
Mass of sulfur in the product = Mass of product - Mass of copper in the product
Mass of sulfur in the product = 0.240 g - 0.192 g = 0.048 g

Percent by mass of sulfur = (mass of sulfur / mass of product) x 100%
Percent by mass of sulfur = (0.048 g / 0.240 g) x 100% = 20%

Therefore, the percent by mass of sulfur in the product is 20%.

(b) To determine the empirical formula of the copper sulfide, we need to convert the masses of copper and sulfur to moles.

Molar mass of copper = 63.55 g/mol
Molar mass of sulfur = 32.06 g/mol

Number of moles of copper = mass of copper / molar mass of copper
Number of moles of copper = 0.192 g / 63.55 g/mol ≈ 0.00302 mol

Number of moles of sulfur = mass of sulfur / molar mass of sulfur
Number of moles of sulfur = 0.048 g / 32.06 g/mol ≈ 0.00150 mol

Next, we divide the number of moles by the smallest number of moles to obtain the simplest ratio of copper to sulfur.

Sulfur has the smallest number of moles (0.00150 mol), so we divide both moles by 0.00150 mol to get the following ratio:

Copper: sulfur = 0.00302 mol / 0.00150 mol ≈ 2 : 1

Therefore, the empirical formula of the copper sulfide is Cu2S.