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To determine the percentage by mass of sodium hydrogen carbonate [tex]\((NaHCO_3)\)[/tex] in a 15.0 gram contaminated sample, we can proceed through the following steps:
### Step 1: Identify Given Masses
- Given mass of the total sample: [tex]\( 15.0 \)[/tex] grams
- Mass of sodium carbonate ([tex]\( Na_2CO_3 \)[/tex]) recovered: [tex]\( 6.35 \)[/tex] grams
### Step 2: Calculate Moles of Sodium Carbonate ([tex]\( Na_2CO_3 \)[/tex])
First, we need to find the molar mass of [tex]\( Na_2CO_3 \)[/tex]:
- Molar mass of [tex]\( Na \)[/tex] (Sodium): [tex]\( 22.99 \)[/tex] g/mol
- Molar mass of [tex]\( C \)[/tex] (Carbon): [tex]\( 12.01 \)[/tex] g/mol
- Molar mass of [tex]\( O \)[/tex] (Oxygen): [tex]\( 16.00 \)[/tex] g/mol
[tex]\[ \text{Molar mass of } Na_2CO_3 = 2 \times 22.99 + 12.01 + 3 \times 16.00 = 105.99 \text{ g/mol} \][/tex]
Now calculate the moles of [tex]\( Na_2CO_3 \)[/tex]:
[tex]\[ \text{Moles of } Na_2CO_3 = \frac{\text{Mass of } Na_2CO_3}{\text{Molar mass of } Na_2CO_3} = \frac{6.35 \text{ grams}}{105.99 \text{ g/mol}} \approx 0.0599 \text{ moles} \][/tex]
### Step 3: Relate Moles of [tex]\( Na_2CO_3 \)[/tex] to Moles of [tex]\( NaHCO_3 \)[/tex]
According to the balanced chemical equation:
[tex]\[ 2 NaHCO_3 \rightarrow Na_2CO_3 + H_2O + CO_2 \][/tex]
This indicates that 2 moles of [tex]\( NaHCO_3 \)[/tex] decompose to produce 1 mole of [tex]\( Na_2CO_3 \)[/tex].
Therefore, the moles of [tex]\( NaHCO_3 \)[/tex] are:
[tex]\[ \text{Moles of } NaHCO_3 = 2 \times \text{Moles of } Na_2CO_3 = 2 \times 0.0599 \text{ moles} = 0.1198 \text{ moles} \][/tex]
### Step 4: Calculate the Mass of Pure [tex]\( NaHCO_3 \)[/tex]
First, we need to find the molar mass of [tex]\( NaHCO_3 \)[/tex]:
- Molar mass of [tex]\( NaHCO_3 \)[/tex]: [tex]\( 84.01 \)[/tex] g/mol
Now calculate the mass of [tex]\( NaHCO_3 \)[/tex]:
[tex]\[ \text{Mass of } NaHCO_3 = \text{Moles of } NaHCO_3 \times \text{Molar mass of } NaHCO_3 = 0.1198 \text{ moles} \times 84.01 \text{ g/mol} \approx 10.07 \text{ grams} \][/tex]
### Step 5: Calculate the Percentage Purity of [tex]\( NaHCO_3 \)[/tex]
Now we can find the percentage by mass of [tex]\( NaHCO_3 \)[/tex] in the original sample:
[tex]\[ \text{Purity percentage} = \left( \frac{\text{Mass of } NaHCO_3}{\text{Total mass of sample}} \right) \times 100\% = \left( \frac{10.07 \text{ grams}}{15.0 \text{ grams}} \right) \times 100\% \approx 67.11\% \][/tex]
So, the purity of the contaminated sample, in terms of sodium hydrogen carbonate ([tex]\( NaHCO_3 \)[/tex]), is approximately [tex]\( 67.11\% \)[/tex].
### Step 1: Identify Given Masses
- Given mass of the total sample: [tex]\( 15.0 \)[/tex] grams
- Mass of sodium carbonate ([tex]\( Na_2CO_3 \)[/tex]) recovered: [tex]\( 6.35 \)[/tex] grams
### Step 2: Calculate Moles of Sodium Carbonate ([tex]\( Na_2CO_3 \)[/tex])
First, we need to find the molar mass of [tex]\( Na_2CO_3 \)[/tex]:
- Molar mass of [tex]\( Na \)[/tex] (Sodium): [tex]\( 22.99 \)[/tex] g/mol
- Molar mass of [tex]\( C \)[/tex] (Carbon): [tex]\( 12.01 \)[/tex] g/mol
- Molar mass of [tex]\( O \)[/tex] (Oxygen): [tex]\( 16.00 \)[/tex] g/mol
[tex]\[ \text{Molar mass of } Na_2CO_3 = 2 \times 22.99 + 12.01 + 3 \times 16.00 = 105.99 \text{ g/mol} \][/tex]
Now calculate the moles of [tex]\( Na_2CO_3 \)[/tex]:
[tex]\[ \text{Moles of } Na_2CO_3 = \frac{\text{Mass of } Na_2CO_3}{\text{Molar mass of } Na_2CO_3} = \frac{6.35 \text{ grams}}{105.99 \text{ g/mol}} \approx 0.0599 \text{ moles} \][/tex]
### Step 3: Relate Moles of [tex]\( Na_2CO_3 \)[/tex] to Moles of [tex]\( NaHCO_3 \)[/tex]
According to the balanced chemical equation:
[tex]\[ 2 NaHCO_3 \rightarrow Na_2CO_3 + H_2O + CO_2 \][/tex]
This indicates that 2 moles of [tex]\( NaHCO_3 \)[/tex] decompose to produce 1 mole of [tex]\( Na_2CO_3 \)[/tex].
Therefore, the moles of [tex]\( NaHCO_3 \)[/tex] are:
[tex]\[ \text{Moles of } NaHCO_3 = 2 \times \text{Moles of } Na_2CO_3 = 2 \times 0.0599 \text{ moles} = 0.1198 \text{ moles} \][/tex]
### Step 4: Calculate the Mass of Pure [tex]\( NaHCO_3 \)[/tex]
First, we need to find the molar mass of [tex]\( NaHCO_3 \)[/tex]:
- Molar mass of [tex]\( NaHCO_3 \)[/tex]: [tex]\( 84.01 \)[/tex] g/mol
Now calculate the mass of [tex]\( NaHCO_3 \)[/tex]:
[tex]\[ \text{Mass of } NaHCO_3 = \text{Moles of } NaHCO_3 \times \text{Molar mass of } NaHCO_3 = 0.1198 \text{ moles} \times 84.01 \text{ g/mol} \approx 10.07 \text{ grams} \][/tex]
### Step 5: Calculate the Percentage Purity of [tex]\( NaHCO_3 \)[/tex]
Now we can find the percentage by mass of [tex]\( NaHCO_3 \)[/tex] in the original sample:
[tex]\[ \text{Purity percentage} = \left( \frac{\text{Mass of } NaHCO_3}{\text{Total mass of sample}} \right) \times 100\% = \left( \frac{10.07 \text{ grams}}{15.0 \text{ grams}} \right) \times 100\% \approx 67.11\% \][/tex]
So, the purity of the contaminated sample, in terms of sodium hydrogen carbonate ([tex]\( NaHCO_3 \)[/tex]), is approximately [tex]\( 67.11\% \)[/tex].
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