Question

Cisplatin, an anticancer drug, has the molecular formula \(\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2} .\) What is the mass (in gram) of one molecule ? (Atomic weights : \(\mathrm{Pt}=195, \mathrm{H}=1.0, \mathrm{~N}=14, \mathrm{Cl}=35.5\) ) (a) \(4.98 \times 10^{-21}\) (b) \(4.98 \times 10^{-22}\) (c) \(6.55 \times 10^{-21}\) (d) \(3.85 \times 10^{-22}\)

Short answer

The mass of one molecule of Cisplatin is approximately \(4.98 \times 10^{-22}\) grams.

Step-by-step solution

Determine the Molecular Mass

To find the mass of one molecule of Cisplatin, calculate its molecular mass by adding up the atomic masses of each atom in the molecule. The formula for Cisplatin is \(\text{Pt}(NH_3)_2Cl_2\). Multiply the atomic mass of each element by the number of atoms of that element in the molecule, and sum all the values together.

Calculate the Molecular Mass

Use the atomic weights given: Pt = 195, H = 1.0, N = 14, Cl = 35.5. The molecular mass of Cisplatin is calculated as follows: \(\text{Molecular Mass} = (\text{Pt}) + 2(2(\text{H}) + (\text{N})) + 2(\text{Cl}) = 195 + 2(2 \times 1.0 + 14) + 2 \times 35.5\).

Perform the Calculation for Molecular Mass

Substitute the atomic weights and perform the arithmetic: \(\text{Molecular Mass} = 195 + 2(2 + 14) + 2 \times 35.5 = 195 + 2 \times 16 + 71 = 195 + 32 + 71 = 298 \text{ u}\).

Convert Molecular Mass to Mass in Grams

Using Avogadro's number (\(6.02 \times 10^{23}\text{ molecules/mol}\) ), convert the molecular mass from atomic mass units to grams: \(\text{Mass of one molecule} = \frac{\text{Molecular Mass in grams/mol}}{\text{Avogadro's number}}\).

Perform the Final Calculation

Substitute the values to get the mass of one molecule in grams: \(\text{Mass of one molecule} = \frac{298 \text{ g/mol}}{6.02 \times 10^{23} \text{ molecules/mol}} \approx 4.955 \times 10^{-22} \text{ g}\).

Key concepts

Molar Mass of Compounds

Understanding the molar mass of compounds is crucial in chemistry, especially when calculating the mass of any given substance involved in a chemical reaction. The molar mass is defined as the mass of one mole of a particular substance and is expressed in grams per mole (g/mol).

To calculate the molar mass of a compound, such as Cisplatin with the formula \( \text{Pt}(\text{NH}_3)_2\text{Cl}_2 \), sum the product of the number of each type of atom in the molecule and the atomic weight of that element. Figures for atomic weight are found on the periodic table and represent the average mass of isotopes relevant to that element, normalized against the mass of a carbon-12 atom. For Cisplatin, the calculation involves the atomic weights of platinum (Pt), nitrogen (N), hydrogen (H), and chlorine (Cl).

Avogadro's Number

A foundational element in the study of chemistry is Avogadro's number, which is approximately \(6.02 \times 10^{23}\) particles per mole. This value, also known as Avogadro's constant, represents the number of atoms, ions, or molecules present in a mole of substance.

The significance of Avogadro's number becomes apparent when transitioning from atomic scales to measurable quantities, as it relates the micro world to the macro world. When calculating the mass of individual molecules from the molar mass, as shown in the calculation of Cisplatin's mass, Avogadro's number allows us to convert between the scale of individual particles and larger amounts that can be measured in the lab.

Atomic Weight

In the context of a compound like Cisplatin, atomic weight is an indispensable value. The atomic weight, sometimes referred to as atomic mass or relative atomic mass, is the weighted average of the masses of the isotopes of an element, as they occur naturally.

The atomic weight for each element is measured on the unified atomic mass unit (u) scale, which is based on a carbon-12 standard where 12 u is the mass of carbon-12. This unit helps scientists use a consistent standard for comparing the masses of different atoms. As seen in the solution for the mass of a Cisplatin molecule, the atomic weights of platinum (195), hydrogen (1.0), nitrogen (14), and chlorine (35.5) are essential in determining the molecule's mass in atomic mass units before converting it to grams using Avogadro's number.

Stoichiometry

At the heart of chemical equations and reactions lies stoichiometry, which deals with the quantitative relationships between reactants and products. Stoichiometry involves calculations that use the molar masses of compounds and Avogadro's number to predict yields, determine reactant ratios, and calculate amounts required or produced in a reaction.

Stoichiometry is also implemented when scaling a reaction from the molecular level to quantities actionable in a lab setting. For instance, determining how many grams of a drug like Cisplatin can be synthesized from a given amount of reactants requires a deep understanding of stoichiometric principles, as the calculations involve the use of the compound's molar mass and the reactant-product ratios outlined in balanced chemical equations.