Question

\(1 \mathrm{~g}\) mixture of equal number of mole of \(\mathrm{Li}_{2} \mathrm{CO}_{3}\) and other metal carbonate \(\left(\mathrm{M}_{2} \mathrm{CO}_{3}\right)\) 1e \(21.6 \mathrm{~mL}\) of \(0.5 \mathrm{~N} \mathrm{HCl}\) for complete neutralisation reaction. What is the approximate atomic weight of the other metal ? (a) 25 (b) 23 (c) 24 (d) 51

Short answer

The approximate atomic weight of the other metal (M) is 24.

Step-by-step solution

Determine moles of HCl required for neutralization

Given that 21.6 mL of 0.5 N HCl is required for neutralization, calculate the number of moles of HCl. Normality (N) is defined as the number of equivalents per liter. The volume should be in liters for the calculation. The formula to calculate moles from normality and volume is: Number of moles of HCl = Normality of HCl × Volume of HCl in liters. Convert the volume from mL to L by dividing by 1000: 21.6 mL = 0.0216 L. Now calculate the moles of HCl: Number of moles of HCl = 0.5 N × 0.0216 L.

Calculate moles of carbonate ions

Since HCl neutralizes the mixture of Li2CO3 and M2(CO3), one mole of HCl reacts with half a mole of any carbonate (CO3^2-). Therefore, the moles of HCl will equal double the moles of carbonate ions. Use the moles of HCl to find the moles of carbonate ions: Moles of CO3^2- = Moles of HCl / 2.

Determine molar mass of the metal carbonates

Knowing that the mixture is 1g and consists of an equal number of moles of Li2CO3 and M2(CO3), the molar mass of both metal carbonates can be calculated. The molar mass of Li2CO3 is a constant (73.89 g/mol), while the molar mass of M2(CO3) needs to be found. The total mass of the carbonates is the sum of the masses of Li2CO3 and M2(CO3), and since they are present in equal moles, we can set up the equation: Mass of Li2CO3 + Mass of M2(CO3) = 1g. Using the molar mass of Li2CO3 and the moles of CO3^2- found in Step 2, calculate the mass of Li2CO3, then derive the mass of M2(CO3) and use it to calculate the molar mass of M2(CO3).

Calculate the approximate atomic weight of the other metal (M)

We are given that the mixture contains equal moles of Li2CO3 and M2(CO3). From the molar mass of M2(CO3) found in Step 3, we can calculate the approximate atomic weight of the metal M by subtracting the mass of carbonate (60 g/mol for CO3^2-) from the molar mass of M2(CO3) and then dividing the result by 2, as there are two moles of M in each mole of M2(CO3).

Key concepts

Understanding Neutralization Reactions

Neutralization reactions involve the reaction of an acid and a base to form water and a salt. They are quintessential in various chemical processes, especially in chemistry-related problem-solving.

In the problem presented, hydrochloric acid (HCl) is neutralizing a mixture of lithium carbonate (Li₂CO₃) and another metal carbonate (M₂CO₃). It's crucial to recognize that every carbonate ion (CO₃^2-) requires two protons (H⁺) to neutralize the charge and form water and carbon dioxide. This stoichiometric relationship is critical in determining the equivalence point, which is essentially the point in the reaction where there are equivalent amounts of acid and base based on their stoichiometry.

Mastering Molar Mass Calculations

The molar mass calculation is a pivotal step in many chemical problems. It involves finding the mass of one mole of a compound or element, typically expressed in grams per mole (g/mol).

To tackle stoichiometry problems like the one in the exercise, understanding how to calculate molar masses is essential. The given mass of the metal carbonates' mixture and the stoichiometric coefficients from the balanced chemical equations enable us to back-calculate the molar mass of the unknown carbonate. By first knowing the molar mass of Li₂CO₃ and the proportion of CO₃^2- ions, we can infer the mass of the unknown metal in each carbonate molecule, which leads us to determine the unknown metal's atomic weight.

Determining the Equivalence Point

The equivalence point is an important concept in titration, where the amount of titrant added is just enough to completely react with the analyte. In the context of the exercise, the equivalence point is reached when the number of moles of HCl added is stoichiometrically equivalent to the number of moles needed to neutralize the carbonate ions present in both metal carbonates.

To find the equivalence point in our exercise, you would use the relationship that each mole of HCl neutralizes half a mole of carbonate ion, as stated in the balanced equation for the neutralization reaction. Once the moles of HCl used are known, calculating the moles of carbonate ions will lead us to the equivalence point. This point, combined with the molar mass calculations, helps to determine the unknown metal's atomic mass.