The use of silica to form slag in the production of...

The use of silica to form slag in the production of phosphorus from phosphate rock was introduced by Robert Boyle more than 300 years ago. When fluorapatite $\left[\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{F}\right]$ is used in phosphorus production, most of the fluorine atoms appear in the (a) If 15$\%$ by mass of the fluorine in $100 . \mathrm{kg}$ of $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3}$ , F forms $\mathrm{SiF}_{4},$ what volume of this gas is collected at 1.00 $\mathrm{atm}$ and the industrial furnace temperature of $1450 .^{\circ} \mathrm{C} ?$ (b) In some facilities, the $\mathrm{SiF}_{4}$ is used to produce sodium hexafluorosilicate (Na_ilif_ ) which is sold for water fluoridation: $2 \mathrm{SiF}_{4}(g)+\mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow$ $$ \mathrm{Na}_{2} \mathrm{SiF}_{6}(a q)+\mathrm{SiO}_{2}(s)+\mathrm{CO}_{2}(g)+2 \mathrm{HF}(a q) $$ How many cubic meters of drinking water can be fluoridated to a level of 1.0 ppm of $\mathrm{F}^{-}$ using the $\mathrm{SiF}_{4}$ produced in part ( a )?

The use of silica to form slag in the production of phosphorus from phosphate rock was introduced by Robert Boyle more than 300 years ago. When fluorapatite $\left[\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{F}\right]$ is used in phosphorus production, most of the fluorine atoms appear in the
(a) If 15$\%$ by mass of the fluorine in $100 . \mathrm{kg}$ of $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3}$ , F forms
$\mathrm{SiF}_{4},$ what volume of this gas is collected at 1.00 $\mathrm{atm}$ and the industrial furnace temperature of $1450 .^{\circ} \mathrm{C} ?$
(b) In some facilities, the $\mathrm{SiF}_{4}$ is used to produce sodium hexafluorosilicate (Na_ilif_ ) which is sold for water fluoridation: $2 \mathrm{SiF}_{4}(g)+\mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow$
$$
\mathrm{Na}_{2} \mathrm{SiF}_{6}(a q)+\mathrm{SiO}_{2}(s)+\mathrm{CO}_{2}(g)+2 \mathrm{HF}(a q)
$$
How many cubic meters of drinking water can be fluoridated to a level of 1.0 ppm of $\mathrm{F}^{-}$ using the $\mathrm{SiF}_{4}$ produced in part ( a )?

Key Concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It involves converting mass to moles using molar masses, applying mole ratios from balanced chemical equations, and then converting back to mass or volume as needed. This concept is essential for determining how much of a product can be formed from a given amount of reactant.

Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, relates the pressure, volume, temperature, and number of moles of a gas. It is used to calculate the volume of a gas when the temperature, pressure, and moles are known. Proper use of the law requires converting temperatures to Kelvin and ensures that the conditions under which a gas is collected are correctly accounted for in volume calculations.

Gas Collection Under Specific Conditions

This concept involves collecting and quantifying gases produced in a chemical reaction under specified conditions of temperature and pressure. It includes using the ideal gas law to compute the volume of gas produced and understanding how deviations from standard conditions can affect the calculated results, making adjustments as necessary.

Dilution Calculations and ppm Concentration

Dilution calculations involve determining how a concentrated solution or compound can be dispersed in a larger volume to achieve a desired concentration, often expressed in parts per million (ppm). In contexts such as water fluoridation, converting between the amount of a substance (like fluoride) and the required volume of water ensures that the final concentration meets regulatory or health standards.

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