Question

Elemental phosphorus exists as molecules of \(\mathrm{P}_{4}\). It reacts with \(\mathrm{Cl}_{2}(g)\) to produce phosphorus pentachloride. (a) Write the balanced chemical equation for this reaction. (b) What mass of phosphorus pentachloride would be produced by the complete reaction of \(15.2 \mathrm{~g}\) of \(\mathrm{P}_{4}\) ?

Short answer

102.25 g of phosphorus pentachloride is produced.

Step-by-step solution

Write the Unbalanced Equation

The problem involves phosphorus (\(\mathrm{P}_{4}\)) reacting with chlorine gas (\(\mathrm{Cl}_{2}\)) to produce phosphorus pentachloride (\(\mathrm{PCl_5}\)). The unbalanced chemical equation is:\[ \mathrm{P}_{4} + \mathrm{Cl}_{2} \rightarrow \mathrm{PCl}_{5} \]

Balance the Chemical Equation

To balance the equation, first balance the phosphorus atoms. There are 4 phosphorus atoms in \(\mathrm{P}_{4}\), so we need 4 \(\mathrm{PCl}_{5}\) molecules to account for 4 phosphorus atoms. Next, balance the chlorine atoms. There are 20 chlorine atoms on the right (from the 4 \(\mathrm{PCl}_{5}\) molecules), so we need 10 \(\mathrm{Cl}_{2}\) molecules on the left.The balanced equation is:\[ \mathrm{P}_{4} + 10 \mathrm{Cl}_{2} \rightarrow 4 \mathrm{PCl}_{5} \]

Determine the Molar Mass of Substances

Calculate the molar masses of \(\mathrm{P}_{4}\) and \(\mathrm{PCl}_{5}\). - \textbf{P}_{4}: Molar mass of phosphorus is 31.0 g/mol. Therefore, molar mass of \(\mathrm{P}_{4}\) is \(4 \times 31.0 = 124.0\) g/mol.- \mathrm{PCl}_{5}: Molar mass of phosphorus is 31.0 g/mol, and molar mass of chlorine is 35.5 g/mol. Therefore, molar mass of \(\mathrm{PCl}_{5}\) is: \(31.0 + 5 \times 35.5 = 208.5\) g/mol.

Calculate Moles of \(\mathrm{P}_{4}\)

Use the given mass of \(\mathrm{P}_{4}\) to calculate the number of moles:\[\text{Moles of } \mathrm{P}_{4} = \frac{15.2 \text{ g}}{124.0 \text{ g/mol}} = 0.1226 \text{ mol} \]

Calculate Moles of \(\mathrm{PCl}_{5}\) Produced

From the balanced equation, 1 mole of \(\mathrm{P}_{4}\) produces 4 moles of \(\mathrm{PCl}_{5}\). Thus, 0.1226 moles of \(\mathrm{P}_{4}\) will produce:\[ 0.1226 \times 4 = 0.4904 \text{ moles of } \mathrm{PCl}_{5} \]

Calculate the Mass of \(\mathrm{PCl}_{5}\)

Use the moles of \(\mathrm{PCl}_{5}\) to find the mass produced:\[\text{Mass of } \mathrm{PCl}_{5} = 0.4904 \text{ moles} \times 208.5 \text{ g/mol} = 102.25 \text{ g} \]

Key concepts

Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and forming of chemical bonds. In the exercise, phosphorus reacts with chlorine gas to create a new compound, phosphorus pentachloride. This process exemplifies a synthesis reaction where simpler reactants combine to form a more complex product. The reactants,

• Phosphorus (\( \mathrm{P}_{4} \)),
• Chlorine gas (\( \mathrm{Cl}_{2} \)),

undergo a reconfiguration of atoms to form phosphorus pentachloride (\( \mathrm{PCl}_{5} \)). Such reactions are critical in creating new substances in chemistry, allowing us to harness different properties and functionalities beneficial across various applications.
Understanding the type of reaction, recognizing reactants and products, and knowing how substances interact is fundamental for deeper chemical comprehension.

Balancing Chemical Equations

Balancing chemical equations is essential to obey the law of conservation of mass. The law states that mass cannot be created or destroyed in a chemical reaction. Thus, we must make sure that the number of each type of atom on the reactant side is equal to the number on the product side.

In the example given, you start by writing the unbalanced equation:\[ \mathrm{P}_{4} + \mathrm{Cl}_{2} \rightarrow \mathrm{PCl}_{5} \]
Counting atoms helps guide balancing efforts. With four phosphorus atoms in \( \mathrm{P}_{4} \), the product must reflect this count. Thus, using four \( \mathrm{PCl}_{5} \), we balance phosphorus. Chlorine atoms are next. With 20 chlorine atoms needed for four \( \mathrm{PCl}_{5} \), ten \( \mathrm{Cl}_{2} \)molecules provide the necessary atoms.
This balanced equation,\[ \mathrm{P}_{4} + 10\mathrm{Cl}_{2} \rightarrow 4\mathrm{PCl}_{5} \], ensures all atoms from reactants are accounted for in the products.
Mastering this skill helps visualize and predict outcomes of chemical reactions, essential for many scientific studies and applications.

Molar Mass Calculations

Molar mass calculations convert between grams of a substance and moles, offering insight into the amount of material present. This is crucial when examining how much of one substance can react with or produce another.

In the exercise, calculating the molar mass for reactants and products is the first step, using atomic masses from the periodic table:

• Each phosphorus atom weighs 31.0 g/mol, so \( \mathrm{P}_{4} \) (4 atoms) has a molar mass of 124.0 g/mol.
• For \( \mathrm{PCl}_{5} \), add the molar mass of phosphorus (31.0 g/mol) to five times the molar mass of chlorine (35.5 g/mol) to yield 208.5 g/mol.

Using these values helps find:

• Number of moles of \( \mathrm{P}_{4} \) from given mass (15.2 g), resulting in 0.1226 moles.
• This produces 0.4904 moles of \( \mathrm{PCl}_{5} \), which translates to 102.25 g using molar mass calculations.

These calculations guide chemists in understanding reactions on a molecular scale and are instrumental in laboratory and industrial processes, ensuring precision in creating new substances.