This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
ScanSolve AI Answer
Step 1: Define variables for the relative abundances. Let x be the relative abundance of ^35Cl. Since there are only two isotopes, the relative abundance of ^37Cl will be (1-x). Step 2: Set up the equation for the average atomic weight. The average atomic weight of an element is calculated by summing the product of each isotope's mass and its relative abundance. Average atomic weight = (mass of ^35Cl × abundance of ^35Cl) + (mass of ^37Cl × abundance of ^37Cl) Given: Average atomic weight of Chlorine = 35.45 Mass of ^35Cl = 34.96 Mass of ^37Cl = 36.98 Substitute these values into the equation: 35.45 = (34.96 × x) + (36.98 × (1-x)) Step 3: Solve the equation for x. 35.45 = 34.96x + 36.98 - 36.98x Combine the terms with x: 35.45 = (34.96 - 36.98)x + 36.98 35.45 = -2.02x + 36.98 Subtract 36.98 from both sides: 35.45 - 36.98 = -2.02x -1.53 = -2.02x Divide by -2.02: x = (-1.53)/(-2.02) x = (1.53)/(2.02) x ≈ 0.75742574 Step 4: Express the relative abundance as a percentage. To convert the decimal abundance to a percentage, multiply by 100\%: x_\% = 0.75742574 × 100\% x_\% ≈ 75.74\% The relative abundance of ^35Cl is approximately 75.74\%.