A Portland cement sample contained 20% SiO2 by weight derived from two silicate compounds. SiO2.2 CaO and SiO2. 3CaO that are present in the cement in the mole ratio 3:4. Determine the percent by weight of each silicate compound in the cement.
0.202 and 0.358
To determine the percent by weight of each silicate compound in the cement, we can follow these steps:
Step 1: Assume the total weight of the cement sample is 100 grams.
Step 2: Calculate the weight of SiO2 in the cement sample:
- SiO2 accounts for 20% of the cement's weight, so it would be 20 grams.
Step 3: Calculate the mole ratio of SiO2.2 CaO and SiO2.3CaO using the given information:
- The mole ratio is 3:4.
- This means that for every 3 moles of SiO2.2CaO, there are 4 moles of SiO2.3CaO.
Step 4: Convert the weight of SiO2 to moles:
- SiO2 has a molar mass of 60.08 g/mol, so 20 grams would be approximately 0.333 mol (20 g / 60.08 g/mol).
Step 5: Use the mole ratio to find the number of moles for each silicate compound:
- Since the mole ratio is 3:4, we'll have 0.25 mol of SiO2.2CaO (0.333 mol * 3/4) and 0.083 mol of SiO2.3CaO (0.333 mol * 1/4).
Step 6: Calculate the weight of each silicate compound:
- SiO2.2CaO has a molar mass of 172.24 g/mol, so the weight would be approximately 43.06 grams (0.25 mol * 172.24 g/mol).
- SiO2.3CaO has a molar mass of 220.29 g/mol, so the weight would be approximately 18.36 grams (0.083 mol * 220.29 g/mol).
Step 7: Calculate the percent by weight of each silicate compound:
- The weight of SiO2.2CaO is 43.06 grams, which is 43.06% of the cement sample's weight (43.06 g / 100 g * 100%).
- The weight of SiO2.3CaO is 18.36 grams, which is 18.36% of the cement sample's weight (18.36 g / 100 g * 100%).
Therefore, the percent by weight of SiO2.2CaO in the cement is approximately 43.06% and the percent by weight of SiO2.3CaO in the cement is approximately 18.36%.
To determine the percent by weight of each silicate compound in the cement, we need to follow these steps:
Step 1: Convert the given weight percentage of SiO2 (20%) to grams.
- Assume we have 100 grams of Portland cement (since weight percentages are usually measured based on 100 grams).
- Therefore, the weight of SiO2 in this sample is 20 grams.
Step 2: Calculate the amount of SiO2.2CaO and SiO2.3CaO compounds in moles.
- The ratio of SiO2.2CaO to SiO2.3CaO is 3:4.
- Let's assume the amount of SiO2.2CaO in moles is 3x, and the amount of SiO2.3CaO in moles is 4x.
- Therefore, the total moles of the two silicate compounds in the cement is 3x + 4x = 7x.
Step 3: Calculate the molar mass of SiO2, CaO, SiO2.2CaO, and SiO2.3CaO.
- SiO2 molar mass: 28.08 g/mol (atomic mass of Si: 28.08 g/mol, atomic mass of oxygen: 16.00 g/mol)
- CaO molar mass: 56.08 g/mol (atomic mass of Ca: 40.08 g/mol, atomic mass of oxygen: 16.00 g/mol)
- SiO2.2CaO molar mass: (28.08 g/mol + 56.08 g/mol) x 2 = 168.32 g/mol
- SiO2.3CaO molar mass: (28.08 g/mol + 56.08 g/mol) x 3 = 252.48 g/mol
Step 4: Calculate the weights of SiO2.2CaO and SiO2.3CaO in the cement.
- Weight of SiO2.2CaO = (3x / 7x) * 7 * 168.32 g
- Weight of SiO2.3CaO = (4x / 7x) * 7 * 252.48 g
Step 5: Simplify the expressions and solve for x.
- Weight of SiO2.2CaO = 3 * 168.32 g = 504.96 g
- Weight of SiO2.3CaO = 4 * 252.48 g = 1009.92 g
Step 6: Calculate the weight percentages of SiO2.2CaO and SiO2.3CaO in the cement.
- Weight percentage of SiO2.2CaO = (Weight of SiO2.2CaO / Total weight of cement) * 100%
- Weight percentage of SiO2.3CaO = (Weight of SiO2.3CaO / Total weight of cement) * 100%
Now, substitute the calculated weights into the formulas:
- Weight percentage of SiO2.2CaO = (504.96 g / 100 g) * 100% = 504.96%
- Weight percentage of SiO2.3CaO = (1009.92 g / 100 g) * 100% = 1009.92%
Since both weight percentages exceed 100%, there may be an error or discrepancy in the provided information or calculations. Please review the given data and calculations to ensure accuracy.