The heads of matches are made with P4S3. this material is made by heating a mixture of red phosphorus and sulfur:
8P4 + 3S8----> 8P4S3
If a match company uses 5435 grams of phosphorous (p4) with an excess of sulfure, how many grams of P4S3 can be made?
1. Convert 5435 g P4 to mols. Remember mols = g/molar mass.
2. Using the coefficients in the balanced equation, convert mols P4 to mols of the product.
3. Now convert mols of the product to grams. Remember g = mols x molar mass.
To determine the number of grams of P4S3 that can be made from 5435 grams of P4, we need to use the given balanced equation:
8P4 + 3S8 → 8P4S3
From the equation, we can see that we need 8 moles of P4 to produce 8 moles of P4S3. Therefore, we need to convert grams of P4 to moles of P4, and then use the mole ratio to calculate moles of P4S3. Finally, we can convert the moles of P4S3 back to grams.
Here are the steps to solve the problem:
Step 1: Find the molar mass of P4.
The molar mass of phosphorus, P4, is calculated as:
4 × molar mass of phosphorus (P)
= 4 × 31.0 g/mol
= 124.0 g/mol
Step 2: Convert grams of P4 to moles of P4 using the molar mass.
Number of moles of P4 = mass of P4 / molar mass of P4
= 5435 g / 124.0 g/mol
= 43.87 mol
Step 3: Calculate the moles of P4S3 using the mole ratio from the balanced equation.
From the balanced equation:
8 moles of P4 produce 8 moles of P4S3
Therefore, 43.87 moles of P4 produce (43.87 moles × 8 moles)/(8 moles) = 43.87 moles of P4S3
Step 4: Convert moles of P4S3 to grams using the molar mass.
Molar mass of P4S3 = (molar mass of P4) × 4 + (molar mass of sulfur, S) × 3
= (124.0 g/mol) × 4 + (32.1 g/mol) × 3
= 496.0 g/mol + 96.3 g/mol
= 592.3 g/mol
Mass of P4S3 = number of moles of P4S3 × molar mass of P4S3
= 43.87 mol × 592.3 g/mol
= 25,955.5 g
Therefore, approximately 25,955.5 grams of P4S3 can be made from 5435 grams of P4 when an excess of sulfur is present.