A rock is 5.0% by mass fayolite(Fe2SiO4), 7.0% by mass forsterite(Mg2SiO4) and the remainder silicon dioxide. What is the mass percent of each element in the rock?
I have the answers but i don't know how to solve the problem.
How would you in steps solve the problem?
Start off by saying lets consider 100 g of rock. Therefore we have
5.0 g Fe2SiO4
7.0 g Mg2SiO4
88.0 g SiO2
lets look at the SiO2. 1 mole of this contains 28 g of Si and 32 g O.
Thus 1 mole or 60 g contains 28 g of Si and 32 g O.
Therefore 88.0 g contains
88.0 g x 28/60 Si = 41 g
88.0 g x 32/60 O = 47 g
Now repeat for the other compounds and add up the masses of each element. Because we chose 100 g to start with then the totals for each element will be the %.
Don't forget to do a check that all the masses add up to 100 g!
To solve this problem, you can follow these steps:
Step 1: Determine the molecular weights of the compounds involved
- Fayolite (Fe2SiO4):
- Atomic mass of Fe = 55.85 g/mol
- Atomic mass of Si = 28.09 g/mol
- Atomic mass of O = 16.00 g/mol
- Molecular weight of Fe2SiO4 = (2 * 55.85) + 28.09 + (4 * 16.00) = 230.73 g/mol
- Forsterite (Mg2SiO4):
- Atomic mass of Mg = 24.31 g/mol
- Atomic mass of Si = 28.09 g/mol
- Atomic mass of O = 16.00 g/mol
- Molecular weight of Mg2SiO4 = (2 * 24.31) + 28.09 + (4 * 16.00) = 140.71 g/mol
- Silicon dioxide (SiO2):
- Atomic mass of Si = 28.09 g/mol
- Atomic mass of O = 16.00 g/mol
- Molecular weight of SiO2 = 28.09 + (2 * 16.00) = 60.09 g/mol
Step 2: Calculate the mass of each compound in the rock
- Mass of Fayolite = 5.0% of total mass of the rock
- Mass of Forsterite = 7.0% of total mass of the rock
- Mass of Silicon dioxide = 100% - (Mass of Fayolite + Mass of Forsterite)
Step 3: Calculate the mass percent of each element in the rock
- Mass percent of Fe = (Mass of Fayolite / Total mass of the rock) * 100
- Mass percent of Mg = (Mass of Forsterite / Total mass of the rock) * 100
- Mass percent of Si = (Mass of Fayolite + Mass of Forsterite + Mass of Silicon dioxide) / Total mass of the rock * 100
- Mass percent of O = (4 * Mass of Fayolite + 4 * Mass of Forsterite + 2 * Mass of Silicon dioxide) / Total mass of the rock * 100
By following these steps, you should be able to calculate the mass percent of each element in the rock.
To solve this problem, follow these steps:
Step 1: Determine the total mass of the rock.
Since the rock is composed of fayolite, forsterite, and silicon dioxide, the sum of their mass percentages will be equal to the total mass of the rock. Let's assume the total mass of the rock is 100 grams.
Step 2: Calculate the mass of each component.
From the problem statement, it is given that the rock is 5.0% fayolite and 7.0% forsterite.
To calculate the mass of fayolite, multiply the mass percentage by total mass:
Mass of Fayolite = (5.0 / 100) * 100 grams = 5 grams.
To calculate the mass of forsterite, multiply the mass percentage by total mass:
Mass of Forsterite = (7.0 / 100) * 100 grams = 7 grams.
Step 3: Calculate the mass of silicon dioxide.
Since the rock contains only these three components and their mass percentages add up to 100%, the remaining mass percentage will be assigned to silicon dioxide:
Mass of Silicon Dioxide = 100% - (5.0% + 7.0%) = 88%.
Therefore, the mass of silicon dioxide is 88 grams.
Step 4: Calculate the mass percentages of each element.
To calculate the mass percentage of each element, divide the mass of each component by the total mass of the rock and multiply by 100%.
Mass Percentage of Fayolite = (Mass of Fayolite / Total mass) * 100%
= (5 grams / 100 grams) * 100% = 5%.
Mass Percentage of Forsterite = (Mass of Forsterite / Total mass) * 100%
= (7 grams / 100 grams) * 100% = 7%.
Mass Percentage of Silicon Dioxide = (Mass of Silicon Dioxide / Total mass) * 100%
= (88 grams / 100 grams) * 100% = 88%.
Therefore, the mass percent of each element in the rock is:
- Fayolite: 5%
- Forsterite: 7%
- Silicon Dioxide: 88%.