Sure, let's go through the steps to determine the mass of NaCl produced from 7.5 grams of Na₂CO₃.
### Step 1: Determine the Molar Mass of Na₂CO₃
First, we need to calculate the molar mass of sodium carbonate (Na₂CO₃):
- Sodium (Na): Atomic mass = 22.99 g/mol. Since there are 2 sodium atoms, the total mass contribution from sodium is [tex]\( 2 \times 22.99 = 45.98 \)[/tex] g/mol.
- Carbon (C): Atomic mass = 12.01 g/mol. Since there is 1 carbon atom, the total mass contribution from carbon is [tex]\( 1 \times 12.01 = 12.01 \)[/tex] g/mol.
- Oxygen (O): Atomic mass = 16.00 g/mol. Since there are 3 oxygen atoms, the total mass contribution from oxygen is [tex]\( 3 \times 16.00 = 48.00 \)[/tex] g/mol.
Adding these together, the molar mass of Na₂CO₃ is:
[tex]\[ 45.98 + 12.01 + 48.00 = 105.99 \, \text{g/mol} \][/tex]
### Step 2: Calculate the Number of Moles of Na₂CO₃
Next, we calculate how many moles of Na₂CO₃ are in 7.5 grams:
[tex]\[ \text{Moles of Na}_2\text{CO}_3 = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{7.5 \, \text{g}}{105.99 \, \text{g/mol}} = 0.07076139258420606 \, \text{moles} \][/tex]
### Step 3: Determine the Moles of NaCl Produced
From the balanced chemical equation, we know that 1 mole of Na₂CO₃ produces 2 moles of NaCl. Therefore, we calculate the moles of NaCl:
[tex]\[ \text{Moles of NaCl} = 2 \times 0.07076139258420606 = 0.14152278516841213 \, \text{moles} \][/tex]
### Step 4: Calculate the Molar Mass of NaCl
Now, we compute the molar mass of sodium chloride (NaCl):
- Sodium (Na): Atomic mass = 22.99 g/mol.
- Chlorine (Cl): Atomic mass = 35.45 g/mol.
Adding these together, the molar mass of NaCl is:
[tex]\[ 22.99 + 35.45 = 58.44 \, \text{g/mol} \][/tex]
### Step 5: Calculate the Mass of NaCl Produced
Finally, we calculate the mass of NaCl produced:
[tex]\[ \text{Mass of NaCl} = \text{Moles} \times \text{Molar Mass} = 0.14152278516841213 \, \text{moles} \times 58.44 \, \text{g/mol} = 8.270591565242004 \, \text{grams} \][/tex]
So, 7.5 grams of Na₂CO₃ will produce approximately 8.27 grams of NaCl.
