Question

Determine the percent composition of \(\mathrm{MgCO}_{3} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) and draw a pie graph to represent the hydrate.

Short answer

To find the percent composition of \(\mathrm{MgCO}_{3} \cdot 5 \mathrm{H}_{2}\mathrm{O}\), calculate the molar mass of the compound using the periodic table: - Mg: 24.305 g/mol - C: 12.011 g/mol - O: 16.00 g/mol - H: 1.008 g/mol Molar mass of \(MgCO_{3} \cdot 5H_{2}O\) = 24.305 + 12.011 + 3(16.00) + 5(2(1.008) + 16.00). Then, calculate the percent compositions of Mg, C, O, and H using the molar masses and draw a pie graph representing the hydrate by labeling each section with the element symbol and percent composition. Ensure that the sum of all percent compositions equals 100%.

Step-by-step solution

Determine the molar masses of the compound and its elements

To begin, we need to calculate the molar mass of \(\mathrm{MgCO}_{3} \cdot 5 \mathrm{H}_{2}\mathrm{O}\). Using the periodic table, we find the following molar masses for each element: - Mg: 24.305 g/mol - C: 12.011 g/mol - O: 16.00 g/mol - H: 1.008 g/mol Now calculate the molar mass of the compound: \[ \text{Molar mass of } \mathrm{MgCO_{3} \cdot 5 H_{2}O} = \mathrm{Mg + C + 3O + 5(2H + O)} \] \[ = 24.305 + 12.011 + 3(16.00) + 5(2(1.008) + 16.00) \]

Calculate the percent compositions

Calculate the percent compositions of Mg, C, O, and H in the compound using the formula: Percent composition = \(\frac{\text{molar mass of element}}{\text{molar mass of compound}} \times 100\) For Mg: \[ \text{%Mg} = \frac{24.305}{24.305 + 12.011 + 3(16.00) + 5(2(1.008) + 16.00)} \times 100 \] For C: \[ \text{%C} = \frac{12.011}{24.305 + 12.011 + 3(16.00) + 5(2(1.008) + 16.00)} \times 100 \] For O: \[ \text{%O} = \frac{3(16.00) + 5(16.00)}{24.305 + 12.011 + 3(16.00) + 5(2(1.008) + 16.00)} \times 100 \] For H: \[ \text{%H} = \frac{5(2(1.008))}{24.305 + 12.011 + 3(16.00) + 5(2(1.008) + 16.00)} \times 100 \]

Draw a pie graph

After calculating the percent compositions, create a pie graph with four sections, one for each element. Label each section with the element's symbol and its corresponding percent composition. To make the pie graph, you can use graphing software tools, or you can draw it by hand using a protractor to measure out the angles for each section. The angles for each section can be found by multiplying the percent compositions by 360°: \[ \text{Angle for an element} = \text{Percent composition} \times \frac{360^\circ}{100} \] Note: It's essential to verify that the sum of all percent compositions equals 100% (or very close to it) before creating the pie graph.

Key concepts

Molar Mass Calculation

Understanding the molar mass of a compound is pivotal in the field of chemistry, particularly when dealing with percent composition exercises. The molar mass represents the mass of one mole of a substance, and it is calculated by summing the masses of the individual elements contained in one mole of the compound. This is usually done by referring to the atomic masses listed on the periodic table for each element.

For instance, in the exercise involving \( \mathrm{MgCO_{3} \cdot 5 H_{2}O} \), the molar mass is found by adding together the masses of magnesium (Mg), carbon (C), oxygen (O), and the water molecules (\( \cdot 5 \mathrm{H}_{2}\mathrm{O} \)). Each element's mass is multiplied by the number of times it appears in the compound. After the individual atomic masses have been tallied, the total sum reflects the molar mass of the entire compound. This fundamental calculation allows us to delve deeper into the analysis of the substance's composition.

Hydrate Composition

A hydrate is a compound that incorporates water molecules into its structure in a definite ratio. In a chemical notation, this is represented by the dot symbol followed by the water composition, as seen in \( \mathrm{MgCO}_{3} \cdot 5 \mathrm{H}_{2}\mathrm{O} \). The \(5\mathrm{H}_{2}\mathrm{O}\) signifies that there are five moles of water for every mole of \(\mathrm{MgCO}_{3}\).

When calculating the percent composition, the molar mass of the water component needs to be taken into account just like any other element in the compound. This means considering the combined mass of hydrogen and oxygen for each mole of water present. In our example, it's critical to not only calculate the mass contributions of Mg, C, and O from \(\mathrm{MgCO}_{3}\), but also include the contribution from the five moles of water bound to the compound.

Pie Graph Representation

After computing the percent compositions of each element in a compound, visualizing this data can be done effectively using a pie graph. A pie graph, or pie chart, breaks down the total into slices, each slice's size being proportional to the percent contribution of each component. For chemistry students, this representation facilitates an intuitive understanding of the distribution of elements within a compound.

To create a pie graph from percent composition data, convert the percentage of each element to an angle by multiplying it by 3.6 (since \(360^\circ\) is the total for a circle). A pie graph is especially helpful because it gives a visual sense of the relative masse of each element in a compound at a glance. Remember, however, to ensure that the percentages add up to 100% or very close to it, to maintain accuracy in your graphical representation.