Questions: Practice - Stoichiometry 1) In a chemical reaction requiring two atoms of phosphorus for five atoms of oxygen, how many grams of oxygen are required by 3.10 g of phosphorus? 2) What mass of sulfur must combine with aluminum to form 600 lbs .(272.4 kg) of aluminum sulfide?

Practice - Stoichiometry
1) In a chemical reaction requiring two atoms of phosphorus for five atoms of oxygen, how many grams of oxygen are required by 3.10 g of phosphorus?
2) What mass of sulfur must combine with aluminum to form 600 lbs .(272.4 kg) of aluminum sulfide?
Transcript text: Practice - Stoichiometry 1) In a chemical reaction requiring two atoms of phosphorus for five atoms of oxygen, how many grams of oxygen are required by 3.10 g of phosphorus? 2) What mass of sulfur must combine with aluminum to form $600 \mathrm{lbs} .(272.4 \mathrm{~kg})$ of aluminum sulfide?
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Solution

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Solution Steps

Step 1: Determine the Molar Masses

First, we need to determine the molar masses of phosphorus (P) and oxygen (O). The atomic masses are approximately:

  • Phosphorus (P): 30.97 g/mol
  • Oxygen (O): 16.00 g/mol
Step 2: Write the Balanced Chemical Equation

The reaction between phosphorus and oxygen can be represented as: \[ 4 \text{P} + 5 \text{O}_2 \rightarrow 2 \text{P}_2\text{O}_5 \]

This equation shows that 4 moles of phosphorus react with 5 moles of oxygen molecules.

Step 3: Calculate Moles of Phosphorus

Given 3.10 g of phosphorus, we calculate the moles of phosphorus: \[ \text{Moles of P} = \frac{3.10 \, \text{g}}{30.97 \, \text{g/mol}} = 0.1001 \, \text{mol} \]

Step 4: Use Stoichiometry to Find Moles of Oxygen

From the balanced equation, 4 moles of phosphorus react with 5 moles of oxygen. Therefore, the moles of oxygen required are: \[ \text{Moles of } \text{O}_2 = 0.1001 \, \text{mol P} \times \frac{5 \, \text{mol } \text{O}_2}{4 \, \text{mol P}} = 0.1251 \, \text{mol } \text{O}_2 \]

Step 5: Calculate Mass of Oxygen

Now, calculate the mass of oxygen required: \[ \text{Mass of } \text{O}_2 = 0.1251 \, \text{mol} \times 32.00 \, \text{g/mol} = 4.0032 \, \text{g} \]

Final Answer

The mass of oxygen required is \(\boxed{4.0032 \, \text{g}}\).


Step 1: Determine the Molar Masses for Aluminum Sulfide

For the second question, we need the molar masses of aluminum (Al) and sulfur (S):

  • Aluminum (Al): 26.98 g/mol
  • Sulfur (S): 32.07 g/mol

The formula for aluminum sulfide is \(\text{Al}_2\text{S}_3\).

Step 2: Write the Balanced Chemical Equation

The reaction between aluminum and sulfur is: \[ 2 \text{Al} + 3 \text{S} \rightarrow \text{Al}_2\text{S}_3 \]

Step 3: Calculate Moles of Aluminum Sulfide

Convert the mass of aluminum sulfide to moles: \[ \text{Molar mass of } \text{Al}_2\text{S}_3 = 2(26.98) + 3(32.07) = 150.14 \, \text{g/mol} \] \[ \text{Moles of } \text{Al}_2\text{S}_3 = \frac{272.4 \, \text{kg} \times 1000 \, \text{g/kg}}{150.14 \, \text{g/mol}} = 1814.3 \, \text{mol} \]

Step 4: Use Stoichiometry to Find Moles of Sulfur

From the balanced equation, 1 mole of \(\text{Al}_2\text{S}_3\) requires 3 moles of sulfur. Therefore, the moles of sulfur required are: \[ \text{Moles of S} = 1814.3 \, \text{mol} \times \frac{3 \, \text{mol S}}{1 \, \text{mol } \text{Al}_2\text{S}_3} = 5442.9 \, \text{mol S} \]

Step 5: Calculate Mass of Sulfur

Now, calculate the mass of sulfur required: \[ \text{Mass of S} = 5442.9 \, \text{mol} \times 32.07 \, \text{g/mol} = 174,500 \, \text{g} = 174.5 \, \text{kg} \]

Final Answer

The mass of sulfur required is \(\boxed{174.5 \, \text{kg}}\).

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