Problem 119 - College Algebra Essentials

Question

The mass of one oxygen molecule is \(5.3 \times 10^{-23}\) gram. Find the mass of \(20,000\) molecules of oxygen. Express the answer in scientific notation.

Step-by-Step Solution

Answer

The mass of \(20,000\) oxygen molecules is \(1.06 \times 10^{-19} g\).

Step 1: Understand the Problem

Given is the mass of one oxygen molecule which is \(5.3 \times 10^{-23}\) gram. The task is to find the mass of \(20,000\) such molecules.

Step 2: Apply Basic Multiplication

To find the total mass, multiply the given mass of one molecule by the number of molecules. This gives \(5.3 \times 10^{-23} g/molecule \times 20000 \, molecules\)

Step 3: Calculation

Multiplying \(5.3 \times 10^{-23}\) by \(20000\) gives \(1.06 \times 10^{-19} g\)

Step 4: Convert to Scientific Notation

Finally, we rewrite this number in scientific notation. We want the number in front of the multiplication sign to be between 1 and 10, so we move the decimal point 2 places to the left which gives \(1.06 \times 10^{-19} g\)