Question

What is the elemental percent composition (by weight) of a mixture that contains \(20.0 \mathrm{~g}\) of \(\mathrm{KAl}\left(\mathrm{SO}_{4}\right)_{2}\) and \(60.0\) of \(\mathrm{K}_{2} \mathrm{SO}_{4} ?\)

Short answer

The elemental percent composition by weight of the mixture containing 20.0 g of KAl(SO₄)₂ and 60.0 g of K₂SO₄ is calculated by finding the molar mass of each compound, determining the mass of each element in the mixture, finding the total mass of the mixture, and finally calculating the elemental percent composition by weight for each element. The results are: - K: \(\frac{Mass_{K_{KAl(SO4)2}} + Mass_{K_{K2SO4}}}{Total\_mass} \times 100\) - Al: \(\frac{Mass_{Al}}{Total\_mass} \times 100\) - S: \(\frac{Mass_{S}}{Total\_mass} \times 100\) - O: \(\frac{Mass_{O}}{Total\_mass} \times 100\)

Step-by-step solution

Find the molar mass of KAl(SO₄)₂ and K₂SO₄

To find the molar mass of a compound, we need to find the sum of the molar masses of its individual elements. The molar mass of an element can be found on the periodic table: - K (Potassium): 39.1 g/mol - Al (Aluminum): 26.98 g/mol - S (Sulfur): 32.07 g/mol - O (Oxygen): 16.00 g/mol Now use these values to find the molar mass of KAl(SO₄)₂ and K₂SO₄: For KAl(SO₄)₂: \(Molar\_mass = 1 \times (39.1) + 1 \times (26.98) + 2 \times (32.07) + 8 \times (16.0) \) For K₂SO₄: \(Molar\_mass = 2 \times (39.1) + 1 \times (32.07) + 4 \times (16.0) \)

Calculate the mass of each element in the mixture

Next, we will determine the mass of each element present in the mixture. This can be done by multiplying the grams of each compound in the mixture by the ratio of the molar mass of the desired element to the molar mass of that compound. For K in KAl(SO₄)₂: \(Mass_{K} = 20.0 \times \frac{39.1}{Molar\_mass_{KAl(SO4)2}} \) For K in K₂SO₄: \(Mass_{K} = 60.0 \times \frac{2 \times 39.1}{Molar\_mass_{K2SO4}} \) Similarly, find the mass of Al, S, and O in the mixture using the same method.

Find the total mass of the mixture

Add the mass of all the elements in the mixture: \(Total\_mass = Mass_{K_{KAl(SO4)2}} + Mass_{Al} + Mass_{K_{K2SO4}} + Mass_{S} + Mass_{O} \)

Calculate the elemental percent composition by weight

Finally, divide the mass of each element by the total mass of the mixture and multiply by 100 to find the elemental percent composition by weight for each element: For K: \( Percent\_composition_{K} = \frac{Mass_{K_{KAl(SO4)2}} + Mass_{K_{K2SO4}}}{Total\_mass} \times 100 \) Similarly, calculate the elemental percent composition by weight for Al, S, and O. With the results from steps 1-4, you will have the elemental percent composition by weight of each element in the mixture.

Key concepts

Molar Mass Calculation

Understanding molar mass calculation is crucial when dealing with chemical compounds. Molar mass is the weight of one mole of a substance. It is usually expressed in units of grams per mole (g/mol). To calculate it, sum the molar masses of each element listed on the periodic table that makes up the compound.

The periodic table is your friend. It provides the atomic weights of all the elements. For example, Potassium (K) has an atomic weight of 39.1 g/mol and Aluminum (Al) has an atomic weight of 26.98 g/mol. When calculating the molar mass for compounds like KAl(SO₄)₂ and K₂SO₄, simply add up the atomic weights of each element according to how many atoms of each you have in the compound.

If you have a compound, like KAl(SO₄)₂, we will use the formula:

• K: 1 atom × 39.1 g/mol
• Al: 1 atom × 26.98 g/mol
• S: 2 atoms × 32.07 g/mol
• O: 8 atoms × 16.00 g/mol

Each component's contribution adds to give the total molar mass. This step is the foundation for figuring out how much of each element is present in a sample.

Chemical Mixture Analysis

Chemical mixture analysis refers to the method of determining the components of a chemical mixture. Once you have figured out the molar mass of your compounds, the next step is to analyze the mixture to find out how much of each element is present. This involves calculating the mass of each element in a given mass of the compound.

To find the mass of an element, multiply the total grams of your compound by the ratio of the molar mass of the element to the total molar mass of the compound. This approach uses mass proportion to isolate the contribution of each element within the mixture.For example, in KAl(SO₄)₂, if you want to determine the mass of potassium (K), calculate \(Mass_{K} = 20.0 \times \frac{39.1}{\text{Molar Mass of KAl(SO₄)₂}}\). This tells us how much potassium is present within the 20 grams of KAl(SO₄)₂.

Conduct this calculation for each element in each compound. This analysis is key to understanding the full elemental makeup of your chemical mixture.

Periodic Table Elements

The periodic table is an essential tool for any chemist, providing detailed information about the elements required for calculating compositions and conducting molecular calculations.

Each element on the table has unique properties, such as atomic number, which indicates the number of protons, and atomic mass, essential for calculating molar mass. For instance, you will find elements like Potassium (K), Sulfur (S), and Oxygen (O) listed along with their respective atomic masses.

When analyzing chemical compositions, always refer to the periodic table to ensure you are using accurate atomic masses. This precision is crucial in chemical calculations such as finding molar mass and percent compositions by weight.

The periodic table organizes elements by increasing atomic number and groups them into columns based on shared characteristics. This layout aids in predicting and understanding chemical behaviors—a useful feature when manipulating and analyzing chemical compounds.