For this problem would I have to use proportions?
Analysis of a metal chloride XCI3 shows that it contains 67.2 % CI by mass. Calculate the molar mass of X and identify the element.
I tried using proportions:
X+CI3/CI3 = ?/67.2
but then I had to find for both X and ?. The question doesn't give the mass of XCI3.
The answers were 51.8g and element Cr
The denominator is 67.2%, means that you can use 100 for the numerator and 67.2 for the denominator.
Proceed the same way as the other problem (Zinc) and post your answer if you are not sure.
I did:
X + CI3/ CI3 = 100/ 67.2
67.2(x+CI3) = 100 CI3
67.2x = 32.8 CI3
x = 0.488 X 100 = 48.8% or grams
Then would I subtract 48.8 from 100 to get 51.2g (would I subtract because I solved for X)?
From 67.2x = 32.8 CI3
you would substitute Cl3 by 3*35.457 (3*atomic mass of chlorine) and solve for x:
x=32.8*35.457/67.2
= 51.92
Look up the periodic table to find the element that has the closest atomic mass.
Chromium is 51.996 compared to 51.92 gives an error of 0.15%.
ok, thank you
You're welcome.
To solve this problem, you don't necessarily need to use proportions. Instead, you can use the concept of molar mass and the given percentage composition.
Here's an explanation of the steps to find the molar mass of X and identify the element:
Step 1: Calculate the molar mass of CI (chlorine):
- The molar mass of CI is approximately 35.45 g/mol. This value can be found on the periodic table.
Step 2: Calculate the molar mass of CI3:
- Since CI3 contains three chlorine atoms, the molar mass of CI3 is calculated by multiplying the molar mass of CI (35.45 g/mol) by 3.
Molar Mass of CI3 = 3 x 35.45 g/mol = 106.35 g/mol
Step 3: Determine the mass of CI in XCl3:
- The problem states that the metal chloride XCI3 contains 67.2% CI by mass. This means that out of every 100 grams of XCI3, 67.2 grams are chlorine.
Step 4: Calculate the mass of X in XCI3:
- Since the remaining percentage (100% - 67.2% = 32.8%) is due to the metal X, the mass of X can be calculated as follows:
Mass of X = 100 g - 67.2 g = 32.8 g
Step 5: Calculate the moles of CI and X in XCl3:
- To calculate the moles of CI and X, divide their respective masses by their molar masses:
Moles of CI = Mass of CI / Molar Mass of CI
Moles of X = Mass of X / Molar Mass of X
Step 6: Calculate the molar mass of X:
- The molar mass of X can be calculated by using the relationship between the moles of CI and moles of X derived from the chemical formula XCI3:
Moles of CI : Moles of X = 3 : 1
- So, you can set up the following equation to find the molar mass of X:
Moles of CI / Moles of X = 3 / 1
(Mass of CI / Molar Mass of CI) / (Mass of X / Molar Mass of X) = 3 / 1
- Substitute the known values:
(67.2 g / 35.45 g/mol) / (32.8 g / Molar Mass of X) = 3
- Rearrange the equation to solve for the molar mass of X:
Molar Mass of X = (67.2 g / 35.45 g/mol) / (32.8 g / Molar Mass of X) * 3
- Now you can plug in the known values to find the molar mass of X.
The above steps should help you calculate the molar mass of X and identify the element.