Problem 61 - Chemistry: The Central Science

Question

A sample of ascorbic acid (vitamin C) is synthesized in the laboratory. It contains \(1.50 \mathrm{~g}\) of carbon and \(2.00 \mathrm{~g}\) of oxygen. Another sample of ascorbic acid isolated from citrus fruits contains \(6.35 \mathrm{~g}\) of carbon. How many grams of oxygen does it contain? Which law are you assuming in answering this question?

Step-by-Step Solution

Answer

The second sample of ascorbic acid contains approximately 4.76 g of oxygen. We have assumed the Law of Constant Composition (Law of Definite Proportions) to solve the problem.

Step 1: Find the mass ratio of carbon and oxygen in the first sample

For the first sample, we are given the mass of carbon (1.50 g) and the mass of oxygen (2.00 g). We find the mass ratio between carbon and oxygen: Mass ratio (C : O) = mass of carbon / mass of oxygen Mass ratio (C : O) = 1.50 g / 2.00 g = \(0.75\)

Step 2: Use the mass ratio to find the mass of oxygen in the second sample

For the second sample, we are given the mass of carbon (6.35 g). We know that the ratio between carbon and oxygen in ascorbic acid remains constant, so we can calculate the mass of oxygen using the same mass ratio: Mass of oxygen = mass of carbon x mass ratio (O : C) Mass of oxygen = 6.35 g x \(0.75\)

Step 3: Calculate the mass of oxygen in the second sample

By multiplying the mass of carbon in the second sample by the mass ratio, we can find the mass of oxygen in the sample: Mass of oxygen = 6.35 g x \(0.75\) = 4.7625 g So, there are approximately 4.76 g of oxygen in the second sample.

Step 4: Identify the law assumed for solving the problem

In answering this question, we assumed the Law of Constant Composition (also known as the Law of Definite Proportions), which states that a given chemical compound always contains the same proportions by mass of its constituent elements.