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examples of scaled mole conversions

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Scaled mole conversions involve converting between different amounts of substances using the concept of moles as a bridge. This often applies in chemistry where reactions and stoichiometry are concerned. Below are some examples demonstrating scaled mole conversions in various contexts:

Example 1: Basic Stoichiometry

Reaction:
\[ 2H_2 + O_2 \rightarrow 2H_2O \]

Question: How many moles of water (H₂O) can be produced from 3 moles of O₂?

Solution:

  1. According to the balanced equation, 1 mole of O₂ produces 2 moles of H₂O.
  2. Therefore, from 3 moles of O₂: \[ 3 , \text{moles O}_2 \times \left(\frac{2 , \text{moles H}_2O}{1 , \text{mole O}_2}\right) = 6 , \text{moles H}_2O \]

Example 2: Molar Mass Conversion

Question: How many moles are in 50 grams of sodium chloride (NaCl)?

Solution:

  1. First, calculate the molar mass of NaCl:

    • Sodium (Na): 23 g/mol
    • Chlorine (Cl): 35.5 g/mol
    • Molar mass of NaCl = 23 g/mol + 35.5 g/mol = 58.5 g/mol

  2. Use the formula: \[ \text{Moles of NaCl} = \frac{\text{mass}}{\text{molar mass}} = \frac{50 , \text{g}}{58.5 , \text{g/mol}} \approx 0.854 , \text{moles NaCl} \]

Example 3: Gas Volume at STP

Question: How many moles of gas are in a 22.4 L container at STP (standard temperature and pressure)?

Solution: Using the molar volume of an ideal gas (22.4 L at STP), we can determine the number of moles: \[ \text{Moles of gas} = \frac{\text{Volume}}{\text{Molar volume}} = \frac{22.4 , \text{L}}{22.4 , \text{L/mol}} = 1 , \text{mole} \]

Example 4: Mixing Solutions

Question: If you mix 2 moles of a 1 M NaCl solution with 1 mole of a 2 M NaCl solution, what is the final concentration of NaCl?

Solution:

  1. Calculate the total amount of NaCl:
    • 1 M solution: 2 moles NaCl
    • 2 M solution: 1 mole NaCl (since 2 M means 2 moles per liter, you have 1 mole in 0.5 L)
  2. Total NaCl = 2 moles + 1 mole = 3 moles
  3. Determine the total volume of the mixed solution:
    • Volume from 1 M solution: 2 L (1 M solution to make 2 moles)
    • Volume from 2 M solution: 0.5 L (to produce 1 mole)
    • Total volume = 2 L + 0.5 L = 2.5 L
  4. Calculate the final concentration: \[ \text{Final concentration} = \frac{3 \text{ moles}}{2.5 \text{ L}} = 1.2 , \text{M} \]

These examples showcase how to use scaled mole conversions to solve various problems related to stoichiometry, molar mass, gas laws, and solution concentrations.