Question

Arrange the compounds in order of decreasing formula mass. $$ \mathrm{WO}_{2}, \mathrm{Rb}_{2} \mathrm{SO}_{4}, \mathrm{~Pb}\left(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right)_{2}, \mathrm{RbI} $$

Short answer

Decreasing order: Pb(C2H3O2)2, Rb2SO4, WO2, RbI.

Step-by-step solution

Calculate the formula mass of WO2

To find the formula mass of tungsten dioxide (WO2), add the atomic mass of tungsten (W) to twice the atomic mass of oxygen (O). The atomic masses are approximately W = 183.84 u and O = 16.00 u. The calculation is as follows: \( 1 \cdot 183.84 \, u + 2 \cdot 16.00 \, u = 183.84 \, u + 32.00 \, u = 215.84 \, u \).

Calculate the formula mass of Rb2SO4

To determine the formula mass of rubidium sulfate (Rb2SO4), add twice the atomic mass of rubidium (Rb) to the atomic mass of sulfur (S) and four times the atomic mass of oxygen (O). The atomic masses are approximately Rb = 85.47 u, S = 32.07 u, and O = 16.00 u. The calculation is as follows: \( 2 \cdot 85.47 \, u + 1 \cdot 32.07 \, u + 4 \cdot 16.00 \, u = 170.94 \, u + 32.07 \, u + 64.00 \, u = 267.01 \, u \).

Calculate the formula mass of Pb(C2H3O2)2

To calculate the formula mass of lead(II) acetate (Pb(C2H3O2)2), add the atomic mass of lead (Pb) to twice the sum of twice the atomic mass of carbon (C), three times the atomic mass of hydrogen (H), and twice the atomic mass of oxygen (O). The atomic masses are Pb = 207.2 u, C = 12.01 u, H = 1.008 u, O = 16.00 u. Thus: \( 1 \cdot 207.2 \, u + 2 \cdot (2 \cdot 12.01 \, u + 3 \cdot 1.008 \, u + 2 \cdot 16.00 \, u) = 207.2 \, u + 2 \cdot (24.02 \, u + 3.024 \, u + 32.00 \, u) = 207.2 \, u + 2 \cdot 59.044 \, u = 207.2 \, u + 118.088 \, u = 325.288 \, u \).

Calculate the formula mass of RbI

The formula mass of rubidium iodide (RbI) is determined by summing up the atomic masses of rubidium (Rb) and iodine (I). The atomic masses are approximately Rb = 85.47 u, I = 126.90 u. Perform the calculation: \( 1 \cdot 85.47 \, u + 1 \cdot 126.90 \, u = 85.47 \, u + 126.90 \, u = 212.37 \, u \).

Arrange in order of decreasing formula mass

Now that we have calculated the formula masses of each compound, we can order them from largest to smallest: Pb(C2H3O2)2 > Rb2SO4 > WO2 > RbI. The final order is: \( \text{Pb}(C_2H_3O_2)_2 (325.288 \, u) > \text{Rb}_2SO_4 (267.01 \, u) > WO_2 (215.84 \, u) > RbI (212.37 \, u) \).

Key concepts

Atomic Mass

Understanding atomic mass is fundamental when calculating the formula mass of substances. Atomic mass, often referred to as atomic weight, is the weighted average mass of an atom of an element based on the natural occurrence of each of its isotopes. Measured in atomic mass units (u), atomic mass serves as a key building block in calculating the mass of molecules.

For instance, in the exercise provided, tungsten (W) has an atomic mass of approximately 183.84 u, while oxygen (O) is 16.00 u. These values are crucial when determining the formula mass of a compound such as tungsten dioxide (WO2). The concept of atomic mass is not only important in finding the mass of a single molecule but also in stoichiometry, where the relative mass of atoms affects the proportions in chemical reactions. Accurate knowledge of atomic masses enables students to predict the amounts of each substance involved in a reaction.

Molecular Weight

Molecular weight, also known as molecular mass, is the sum of the atomic masses of all atoms in a molecule. It is calculated by adding together the atomic mass of each element, multiplied by the number of times that element appears in the molecule.

In the given exercise, the molecular weight of rubidium sulfate (Rb2SO4) is obtained by summing up the atomic masses of two rubidium atoms, one sulfur atom, and four oxygen atoms. The pivotal aspect of understanding molecular weight lies in its application. It is not only applicable in laboratory settings for measuring quantities but also essential in stoichiometric calculations, which involve the ratios of reactants and products in chemical reactions. By knowing the molecular weight, one can accurately convert between moles and grams, which is a critical skill in any chemistry-related field.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It relies heavily on the concept of the mole and the conservation of mass and charges during reactions.

Utilizing the calculated formula masses from the exercise, stoichiometry could simplify complex chemical equations to more manageable proportions and help in deducing the amounts of substances produced or required in a given reaction. The stoichiometric coefficients, which indicate the number of moles of each substance that participates in a reaction, are influenced by the formula masses of the involved compounds. For students, mastering stoichiometry is vital to correctly interpret and balance chemical equations and to engage in quantitative chemical analysis.