Reaction Stoichiometry 747 Gallium Chloride Is Formed By The ✓ Solved

Reaction Stoichiometry747 Gallium Chloride Is Formed By The Reaction

Reaction Stoichiometry 7.47. Gallium chloride is formed by the reaction of 2.6 L of a 1.44 M solution of HCl according to the following equation: 2Ga + 6HCl → 2GaCl₃ + 3H₂. (a) Outline the steps necessary to determine the number of moles and mass of gallium chloride. (b) Perform the calculations outlined Enthalpy 9.51. A sample of 0.562 g of carbon is burned in oxygen in a bomb calorimeter, producing carbon dioxide. Assume both the reactants and products are under standard state conditions, and that the heat released is directly proportional to the enthalpy of combustion of graphite. The temperature of the calorimeter increases from 26.74 °C to 27.93 °C. What is the heat capacity of the calorimeter and its contents?

Sample Paper For Above instruction

The process of determining the amount of gallium chloride formed from a given reaction mixture involves several key steps rooted in stoichiometry and molar calculations. First, identify the reaction equation and the known quantities of reactants utilized—specifically, the volume and molarity of hydrochloric acid (HCl). Then, convert the volume of HCl to moles using the molarity. Given the balanced chemical equation, establish the molar ratios between HCl and GaCl₃ to determine the moles of gallium chloride produced. Afterwards, calculate the mass of gallium chloride by multiplying the moles of GaCl₃ by its molar mass. These steps facilitate the transition from solution volume to the mass of the product formed.

Applying this to the specific problem, begin by calculating moles of HCl: the volume of 2.6 liters and molarity of 1.44 mol/L give the initial moles of HCl. Using the molar ratio from the balanced equation (6 mol HCl : 2 mol GaCl₃), determine the moles of GaCl₃ formed. Mathematically, the moles of HCl are: 2.6 L × 1.44 mol/L = 3.744 mol. The molar ratio then yields: 3.744 mol HCl × (2 mol GaCl₃ / 6 mol HCl) = 1.248 mol GaCl₃. To find the mass, multiply the moles of GaCl₃ by its molar mass (approximately 278.58 g/mol), resulting in: 1.248 mol × 278.58 g/mol ≈ 347.83 grams of gallium chloride.

Regarding the enthalpy calculation involving the combustion of carbon in a bomb calorimeter, the relationship between heat released and temperature change is fundamental. The heat capacity of the calorimeter (C) can be derived from the known heat released during combustion and the observed temperature increase. The first step involves recognizing that the heat released (q) equals the product of the calorimeter's heat capacity and the temperature change: q = C × ΔT. Under standard conditions, the enthalpy of combustion of graphite is roughly -394 kJ/mol. Using the mass of carbon burned, convert this mass to moles: 0.562 g / 12.01 g/mol ≈ 0.0468 mol. The total heat released then is: 0.0468 mol × 394 kJ/mol ≈ 18.45 kJ. The temperature change (ΔT) equals 27.93 °C - 26.74 °C = 1.19 °C. Solving for the heat capacity yields: C = q / ΔT ≈ 18,450 J / 1.19 °C ≈ 15,513 J/°C. This value represents the heat capacity of the calorimeter and its contents, encompassing the calorimeter's material and the contained water or other substances.

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