Question

Calculate the mass in grams of \(1.35 \mathrm{~mol}\) of (a) titanium white, \(\mathrm{TiO}_{2}\), used as a paint pigment. (b) sucralose, \(\mathrm{C}_{12} \mathrm{H}_{19} \mathrm{O}_{8} \mathrm{Cl}_{3},\) the active ingredient in the artificial sweetener, Splenda \(^{\mathrm{TM}}\). (c) strychnine, \(\mathrm{C}_{21} \mathrm{H}_{22} \mathrm{~N}_{2} \mathrm{O}_{2},\) present in rat poison.

Short answer

Question: Calculate the mass in grams of 1.35 moles of: (a) titanium dioxide (TiO2), (b) sucralose (C12H19O8Cl3), and (c) strychnine (C21H22N2O2). Answer: (a) 107.82 grams of titanium dioxide (TiO2), (b) 537.28 grams of sucralose (C12H19O8Cl3), and (c) 451.45 grams of strychnine (C21H22N2O2) are present in 1.35 moles of each substance.

Step-by-step solution

(a) Calculate molecular weight of titanium dioxide (TiO2)

To calculate the molecular weight of \(\mathrm{TiO}_{2}\), we first determine the atomic weight of each element involved. Titanium (Ti): 47.87 g/mol Oxygen (O): 16.00 g/mol Now, we calculate the molecular weight: \(\mathrm{TiO}_{2}\) = 1 * (47.87) + 2 * (16.00) = 47.87 + 32.00 = 79.87 g/mol

(a) Calculate mass of titanium dioxide (TiO2)

Now that we have calculated the molecular weight of \(\mathrm{TiO}_{2}\), we can calculate the mass in grams using the formula: Mass (grams) = Moles x Molecular weight (M) Mass (grams) = 1.35 * 79.87 = 107.82 grams So, there are 107.82 grams of titanium dioxide in 1.35 moles.

(b) Calculate molecular weight of sucralose (C12H19O8Cl3)

To calculate the molecular weight of sucralose, we first determine the atomic weight of each element involved. Carbon (C): 12.01 g/mol Hydrogen (H): 1.008 g/mol Oxygen (O): 16.00 g/mol Chlorine (Cl): 35.45 g/mol Now, we calculate the molecular weight: \(\mathrm{C}_{12} \mathrm{H}_{19} \mathrm{O}_{8}\mathrm{Cl}_{3}\) = 12 * (12.01) + 19 * (1.008) + 8 * (16.00) + 3 * (35.45) = 144.12 + 19.15 + 128.00 + 106.35 = 397.62 g/mol

(b) Calculate mass of sucralose (C12H19O8Cl3)

Now that we have calculated the molecular weight of sucralose, we can calculate the mass in grams using the formula: Mass (grams) = Moles x Molecular weight (M) Mass (grams) = 1.35 * 397.62 = 537.28 grams So, there are 537.28 grams of sucralose in 1.35 moles.

(c) Calculate molecular weight of strychnine (C21H22N2O2)

To calculate the molecular weight of strychnine, we first determine the atomic weight of each element involved. Carbon (C): 12.01 g/mol Hydrogen (H): 1.008 g/mol Nitrogen (N): 14.01 g/mol Oxygen (O): 16.00 g/mol Now, we calculate the molecular weight: \(\mathrm{C}_{21} \mathrm{H}_{22} \mathrm{~N}_{2}\mathrm{O}_{2}\) = 21 * (12.01) + 22 * (1.008) + 2 * (14.01) + 2 * (16.00) = 252.21 + 22.18 + 28.02 + 32.00 = 334.41 g/mol

(c) Calculate mass of strychnine (C21H22N2O2)

Now that we have calculated the molecular weight of strychnine, we can calculate the mass in grams using the formula: Mass (grams) = Moles x Molecular weight (M) Mass (grams) = 1.35 * 334.41 = 451.45 grams So, there are 451.45 grams of strychnine in 1.35 moles.

Key concepts

Molecular Weight

Understanding the molecular weight of a compound is essential for converting moles to mass in chemistry. Molecular weight, also known as molecular mass, is the sum of the atomic weights of all atoms in a molecule expressed in grams per mole (g/mol).

For instance, the molecular weight of titanium dioxide, \( \mathrm{TiO}_{2} \), is calculated by adding the atomic mass of titanium (Ti), which is 47.87 g/mol, to twice the atomic mass of oxygen (O), which is 16.00 g/mol. By multiplying the atomic weight of oxygen by two—since there are two oxygen atoms in the compound—we get:\[ \mathrm{Molecular\ Weight\ of\ TiO}_{2} = 1 \times 47.87 + 2 \times 16.00 = 79.87 \ g/mol \]
To convert moles to mass, we multiply the number of moles by this molecular weight, thus quantifying the substance in grams, which is a more tangible unit of measure for practical laboratory work.

Stoichiometry

Stoichiometry is the aspect of chemistry that pertains to the quantitative relationships between the reactants and products in a chemical reaction. It helps chemists predict the amounts of substances consumed and produced in a given reaction.

Using the principles of stoichiometry, we can calculate the required amount of a substance when its quantity is given in moles. For example, the mass of titanium dioxide required for a reaction can be calculated by using the formula: \( \text{Mass (grams)} = \text{Moles} \times \text{Molecular weight (M)} \).

When we know the molecular weight of the substance and the amount in moles, stoichiometry allows us to accurately determine the mass. It is crucial in chemistry to ensure that the correct proportions of ingredients are used for reactions to proceed as intended. Poor stoichiometric calculations can lead to incomplete reactions, excess of unwanted byproducts, or even hazardous conditions in the laboratory.

Chemical Formulas

Chemical formulas are symbolic representations of the composition of a substance. They denote the types and numbers of atoms that make up a molecule. This information is vital when calculating the molecular weight and, in turn, converting moles to mass.

For instance, the chemical formula for sucralose, \( \mathrm{C}_{12}\mathrm{H}_{19}\mathrm{O}_{8}\mathrm{Cl}_{3} \), indicates it is composed of 12 carbon atoms, 19 hydrogen atoms, 8 oxygen atoms, and 3 chlorine atoms. To find the molecular weight of sucralose, we sum the atomic weights of all these atoms based on their frequency within the molecule:\[ \mathrm{Molecular\ Weight\ of\ Sucralose} = 12 \times 12.01 + 19 \times 1.008 + 8 \times 16.00 + 3 \times 35.45 = 397.62 \ g/mol \].
Understanding chemical formulas is also critical for interpreting and balancing chemical equations, which is a fundamental skill in the study of chemistry.