Question

Arrange the following compounds in the correct order of percentage of metallic element. (a) potassium hydroxide (b) potassium carbonate (c) potassium bicarbonate (d) potassium sulphide (a) \(\mathrm{a}>\mathrm{b}>\mathrm{c}>\mathrm{d}\) (b) \(b>a>c>d\) (c) \(c>b>a>d\) (d) \(\mathrm{d}>\mathrm{a}>\mathrm{b}>\mathrm{c}\)

Short answer

Question: Arrange the given compounds in the correct order of percentage of potassium: (a) Potassium Hydroxide (KOH), (b) Potassium Carbonate (K2CO3), (c) Potassium Bicarbonate (KHCO3), and (d) Potassium Sulphide (K2S). Solution: Upon calculating the percentage of potassium in each compound, we find the following order: Potassium Sulphide (70.9%) > Potassium Hydroxide (69.7%) > Potassium Carbonate (56.6%) > Potassium Bicarbonate (39.1%). Answer: (d) > (a) > (b) > (c)

Step-by-step solution

Determine the molar mass of each compound

We need to know the molar mass of each compound to calculate the percentage of potassium in each. We can find the molar mass by summing the atomic masses of the elements in each compound. (a) Potassium Hydroxide (KOH): Molar mass(K) + Molar mass(O) + Molar mass(H) = 39.1 + 16 + 1 = 56.1 g/mol (b) Potassium Carbonate (K2CO3): (2 x Molar mass(K)) + Molar mass(C) + (3 x Molar mass(O)) = (2 x 39.1) + 12 + (3 x 16) = 78.2 + 12 + 48 = 138.2 g/mol (c) Potassium Bicarbonate (KHCO3): Molar mass(K) + Molar mass(H) + Molar mass(C) + (3 x Molar mass(O)) = 39.1 + 1 + 12 + (3 x 16) = 39.1 + 1 + 12 + 48 = 100.1 g/mol (d) Potassium Sulphide (K2S): (2 x Molar mass(K)) + Molar mass(S) = (2 x 39.1) + 32 = 78.2 + 32 = 110.2 g/mol

Calculate the percentage of potassium in each compound

Now that we have the molar masses of each compound, we can calculate the percentage of potassium in each by dividing the molar mass contributed by potassium by the total molar mass of the compound, and then multiplying by 100. (a) Potassium Hydroxide (KOH): (39.1 / 56.1) x 100 = 69.7% (b) Potassium Carbonate (K2CO3): (78.2 / 138.2) x 100 = 56.6% (c) Potassium Bicarbonate (KHCO3): (39.1 / 100.1) x 100 = 39.1% (d) Potassium Sulphide (K2S): (78.2 / 110.2) x 100 = 70.9%

Compare the percentages and determine the order

Based on our calculations, we have the following order in terms of the percentage of potassium: Potassium Sulphide (70.9%) > Potassium Hydroxide (69.7%) > Potassium Carbonate (56.6%) > Potassium Bicarbonate (39.1%) Hence, the correct answer is (d) \(\mathrm{d}>\mathrm{a}>\mathrm{b}>\mathrm{c}\).

Key concepts

Molar Mass Calculation

Understanding the molar mass of a compound is crucial when it comes to studying chemistry. The molar mass refers to the mass of one mole of a substance, usually expressed in grams per mole (g/mol). One mole of any substance contains Avogadro's number of particles (atoms, molecules, ions, etc.), which is approximately \(6.022 \times 10^{23}\) entities.

To calculate the molar mass of a compound, you simply add together the atomic masses of each element within it, which are presented on the periodic table. It's important to remember that the atomic mass must be multiplied by the number of times the element appears in the chemical formula. For example, in the case of Potassium Hydroxide (KOH), the atomic mass of potassium (K) is 39.1, of oxygen (O) is 16, and of hydrogen (H) is 1. So, their sum \(39.1 + 16 + 1\) gives us the molar mass of KOH, which is 56.1 g/mol.

In chemical calculations, knowing the molar mass is essential as it allows you to convert between the mass of a substance and the number of moles, a foundational aspect of stoichiometry and chemical reactions.

Percentage of Metallic Element

When working with compounds that include metallic elements, it's often necessary to calculate the metallic element's percentage composition within that compound. This is a common requirement in chemistry problems, such as determining the purity of a sample or comparing different compounds containing the same metallic element.

The percentage of a metallic element in a compound is calculated by dividing the total atomic mass of the metallic element in one mole of the compound by the compound's molar mass and then multiplying the result by 100 to get a percentage. In the exercise, for example, Potassium Sulphide (K2S) contains two potassium atoms. You would find the percentage of potassium by taking twice the atomic mass of potassium \((2 \times 39.1)\), dividing it by the molar mass of the compound \(110.2 g/mol\), and multiplying by 100 to get 70.9%. This concept is used to identify the compound with the highest or lowest concentration of a particular metallic element, which is particularly useful in materials science and metallurgy.

Chemical Formula of Compounds

Chemical formulas provide a lot of information in a concise format. They indicate the types of atoms present in a compound and the exact number of each type. In the context of our examples, the formula \(KOH\) tells us that each molecule of potassium hydroxide contains one potassium atom, one oxygen atom, and one hydrogen atom.

Understanding the chemical formula is fundamental when performing molar mass calculations, as it allows you to efficiently account for all elements. For instance, the chemical formula \(K_2CO_3\) for potassium carbonate makes it clear that each unit of this compound contains two potassium atoms, one carbon atom, and three oxygen atoms. This detailed representation helps in making precise calculations regarding the compound's characteristics, such as molar mass and percentage composition.

Chemical formulas are the language of chemistry, vital for communication among scientists and a pillar for calculations in numerous chemical applications, from balancing reactions to determining the theoretical yields in synthesis.