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In order to help prevent tooth decay, fluoride ions at a level of 0.9 mg L$^{-1}$ of F$^-$ are added to Melbourne's public water supplies - VCE - SSCE Chemistry - Question 4 - 2004 - Paper 1

Question 4

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In order to help prevent tooth decay, fluoride ions at a level of 0.9 mg L$^{-1}$ of F$^-$ are added to Melbourne's public water supplies. The fluoride ions are obta... show full transcript

Worked Solution & Example Answer:In order to help prevent tooth decay, fluoride ions at a level of 0.9 mg L$^{-1}$ of F$^-$ are added to Melbourne's public water supplies - VCE - SSCE Chemistry - Question 4 - 2004 - Paper 1

Step 1

i. Calculate the mass of sodium fluoride in mg that must be present in one litre of water to produce a concentration of fluoride ions of 0.90 mg L$^{-1}$.

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Answer

To find the mass of sodium fluoride (NaF) needed:

First, identify the molar mass of NaF:
- Molar mass of Na = 22.99 g/mol
- Molar mass of F = 19.00 g/mol
- Molar mass of NaF = 22.99 + 19.00 = 41.99 g/mol
Using the concentration of fluoride ions:
- We want a concentration of 0.90 mg L $^{-1}$ in 1 L of water.
- Therefore, the mass of fluoride ions required = 0.90 mg.
From the molecular formula, 1 mole of NaF gives 1 mole of fluoride ions. Thus:
- 1 mole of fluoride ions = 41.99 g of NaF.
- Therefore, 0.90 mg of fluoride ions corresponds to:
$ext{mass of NaF} = rac{0.90 ext{ mg} imes 41.99 ext{ g/mol}}{19.00 ext{ g/mol}}$
- Converting 0.90 mg to grams: 0.90 mg = 0.00090 g,
- Calculate:
$ext{mass of NaF} = rac{0.00090 ext{ g} imes 41.99 ext{ g/mol}}{19.00 ext{ g/mol}} \\ ext{mass of NaF} = 0.00197 ext{ g} = 1.97 ext{ mg}$

Thus, the mass of sodium fluoride required is approximately 1.97 mg.

Step 2

ii. What mass of sodium fluoride, in kilogram, must be added to a 750 ML reservoir (1 ML = 10$^{6}$ L) to produce a concentration of fluoride ions of 0.90 mg L$^{-1}$?

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Answer

To determine the mass of sodium fluoride required in a 750 ML reservoir:

First, convert 750 ML to liters:
- 750 ML = 0.750 L.
The concentration of fluoride ions required is 0.90 mg L $^{-1}$ , therefore the total mass of fluoride ions needed in 0.750 L is:

$ext{mass of F} = 0.90 ext{ mg/L} imes 0.750 ext{ L} = 0.675 ext{ mg}$
Now, calculate the corresponding mass of NaF needed:

$ext{mass of NaF} = rac{0.675 ext{ mg} imes 41.99 ext{ g/mol}}{19.00 ext{ g/mol}}$
- Converting mg to grams:
$= 0.000675 ext{ g} imes rac{41.99}{19.00}$

This results in:

$ext{mass of NaF} = 1.48 ext{ mg} = 0.00148 ext{ g} = 0.00000148 ext{ kg}$

Thus, the mass of sodium fluoride required is approximately 0.00000148 kg.

Step 3

iii. Calculate the number of fluoride ions swallowed by a person who drank one litre of water from the reservoir.

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Answer

To calculate the number of fluoride ions in one litre of water:

Recall the concentration of fluoride ions is 0.90 mg L $^{-1}$ .
Convert this mass to grams:
- 0.90 mg = 0.00090 g.
Calculate the moles of fluoride ions:

$ext{moles of F} = rac{ ext{mass}}{ ext{molar mass}} = rac{0.00090 ext{ g}}{0.019 ext{ g/mol}}$
- Calculating:
$ext{moles of F} = 0.04737 ext{ mol}$
Use Avogadro's number to find the number of fluoride ions:

$ext{number of F ions} = 0.04737 ext{ mol} imes 6.022 imes 10^{23} ext{ ions/mol}$
- Calculating:
$ext{number of F ions} ext{ is approximately } 2.85 imes 10^{22} ext{ ions}$ .

Thus, a person who drank one litre of water from the reservoir would swallow approximately $2.85 imes 10^{22}$ fluoride ions.

In order to help prevent tooth decay, fluoride ions at a level of 0.9 mg L$^{-1}$ of F$^-$ are added to Melbourne's public water supplies - VCE - SSCE Chemistry - Question 4 - 2004 - Paper 1

Worked Solution & Example Answer:In order to help prevent tooth decay, fluoride ions at a level of 0.9 mg L$^{-1}$ of F$^-$ are added to Melbourne's public water supplies - VCE - SSCE Chemistry - Question 4 - 2004 - Paper 1

i. Calculate the mass of sodium fluoride in mg that must be present in one litre of water to produce a concentration of fluoride ions of 0.90 mg L$^{-1}$.

ii. What mass of sodium fluoride, in kilogram, must be added to a 750 ML reservoir (1 ML = 10$^{6}$ L) to produce a concentration of fluoride ions of 0.90 mg L$^{-1}$?

iii. Calculate the number of fluoride ions swallowed by a person who drank one litre of water from the reservoir.

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