Potash is any potassium mineral that is used for its...

Potash is any potassium mineral that is used for its potassium content. Most of the potash produced in the United States goes into fertilizer. The major sources of potash are potassium chloride $(\mathrm{KCl})$ and potassium sulfate $\left(\mathrm{K}_{2} \mathrm{SO}_{4}\right) .$ Potash production is often reported as the potassium oxide $\left(\mathrm{K}_{2} \mathrm{O}\right)$ equivalent or the amount of $\mathrm{K}_{2} \mathrm{O}$ that could be made from a given mineral. (a) If $\mathrm{KCl}$ costs $\$ 0.55$ per $\mathrm{kg}$, for what price (dollar per $\mathrm{kg}$ ) must $\mathrm{K}_{2} \mathrm{SO}_{4}$ be sold to supply the same amount of potassium on a per dollar basis? (b) What mass (in kg) of $\mathrm{K}_{2} \mathrm{O}$ contains the same number of moles of $\mathrm{K}$ atoms as $1.00 \mathrm{~kg}$ of KCl?

Potash is any potassium mineral that is used for its potassium content. Most of the potash produced in the United States goes into fertilizer. The major sources of potash are potassium chloride $(\mathrm{KCl})$ and potassium sulfate $\left(\mathrm{K}_{2} \mathrm{SO}_{4}\right) .$ Potash production is often reported as the potassium oxide $\left(\mathrm{K}_{2} \mathrm{O}\right)$ equivalent or the amount of $\mathrm{K}_{2} \mathrm{O}$ that could be made from a given mineral.
(a) If $\mathrm{KCl}$ costs $\$ 0.55$ per $\mathrm{kg}$, for what price (dollar per $\mathrm{kg}$ ) must $\mathrm{K}_{2} \mathrm{SO}_{4}$ be sold to supply the same amount of potassium on a per dollar basis?
(b) What mass (in kg) of $\mathrm{K}_{2} \mathrm{O}$ contains the same number of moles of $\mathrm{K}$ atoms as $1.00 \mathrm{~kg}$ of KCl?

Key Concepts

Equivalent Conversions (K2O Equivalent)

The concept of using equivalence, such as the potassium oxide (K2O) equivalent, provides a standard measure to compare the nutrient value of different potassium-containing compounds. This method facilitates the assessment of fertilizer quality by expressing the potassium content in a uniform chemical form, thereby simplifying comparisons and economic evaluations.

Chemical Stoichiometry

Chemical stoichiometry involves the use of balanced chemical equations to determine the relative quantities of reactants and products. In fertilizer chemistry, stoichiometry is essential for converting between different compounds such as KCl, K2SO4, and K2O, thereby allowing chemists to calculate the precise nutrient content available from various chemical sources.

Potash and Fertilizer Chemistry

Potash refers to potassium-rich minerals that are primarily used in fertilizer production to supply plants with the essential nutrient potassium. In the context of agriculture, understanding the form and content of potash is crucial for efficient fertilizer formulation and ensuring that crops receive the correct amount of potassium for optimal growth.

Molar Mass and Mole Calculations

Calculating molar masses and converting between mass and moles is fundamental in chemistry for quantifying the amount of substance present in different chemical compounds. This concept enables the determination of how many moles of potassium are found in various compounds, which is critical when comparing their nutrient contributions.

Transcript

00:01 Given information for part a, the price of kcl potassium chloride for potassium production is 0 .55 per kg.

00:45 We have to calculate for what price potassium sulfate must be solved to produce the same.

00:54 Amount of potassium on a per dollar basis so first we have to find the mass percentage of potassium in potassium chloride and potassium sulfate the molar mass of kcel is potassium chloride chloride is equal to molar mass of potassium plus molar mass of chlorine is equal to 39 .08 gram per mole plus 35 .453 gram per mole is equal to 74 .551 gram per mole.

02:30 Hence, the mass percent of potassium, the mass percent of potassium in kcl is equal to to molar mass of potassium divided by molar mass of potassium chloride into 100 percent is equal to 39 .098 gram per mole divided by 74 .551 gram per mole into 100 % is equal to 52 .44 % is the mass percent of potassium in case of and the molar mass of k2 -azo4 potassium sulfate is equal to 2 into molar mass of potassium plus smaller mass of sulfur plus 4 into molar mass of oxygen is equal to 2 into 39 .098 gram per mole plus molar mass of sulfur is 32 .065 gram per mole plus 4 into molar mass of oxygen is 15 .999 gram per mole is equal to 174 .257 grams per mole.

05:10 Mass percent of potassium in k2 -so4 is equal to 2 into molar mass of potassium divided by molar mass of the compound k2 -sof -4 into 100 percent is equal to 2 into molar mass of potassium 78 .196 gram per mole divided by molar mass of the compound k2 .4 is 174 .257 gram per mole in 200 % is equal to 44 .487 % and and next we have since the price of kcl is 0 .55 per kg and it contains 52 .44 % of potassium.

06:36 The price of k2 -so4 should be the price of k2 -sof -4 is equal to the price of potassium chloride into.

06:59 The mass percent of potassium in k2 -so4 divided by the mass percent of k in kcl is equal to $0 .558 per kg into 44 .87 percent percent percent divided by 52 .44 % is equal to $0 .47 per cage is the price of k2 -so4.

08:21 Because the price of kcl is 0 .55 per kg and it contains 52 .44 % of potassium.

08:32 The price of k2 s .4 should be 0 .47 per kage.

08:47 And given information for part b, the mass of kcl, mass of kcl is equal to 1 .00 kilogram is equal to 1 .00 into 10 to the power 3 grams.

09:16 And we have to find the mass of k2o that contains the same number of moles of potassium atoms in a given amount of kcl.

09:30 So first we will find the number of the number of moles of kcl.

09:50 So number of moles of kcl is equal to mass of kcl divided by molar mass of kcl is equal to mass of potassium chloride is 1 .00 into 10 brush to the power 3 gram divided by molar mass of potassium chloride is 74 .551 gram per mole is equal to to 13 .41 mole...

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