Question

At a pressure of one billionth (10-9) of atmospheric pressure, there are about 2.7 × 1010 molecules in one cubic centimeter of a gas. How many molecules is this per cubic meter?

1) 2.7 × 1016
2) 2.7 × 1014
3) 2.7 × 1012
4) 2.7 × 108
5) 2.7 × 104

Answer 1

When converting 2.7 × 10ⁱ⁰ molecules from one cubic centimeter to one cubic meter, you multiply by 1,000,000, resulting in 2.7 × 10⁶ molecules per cubic meter.

Step-by-step explanation:

To convert the number of molecules from one cubic centimeter to one cubic meter, we need to consider the volume conversion factor between the two units. There are 1,000,000 cubic centimeters in one cubic meter. Therefore, if there are 2.7 × 10¹⁰ molecules in one cubic centimeter, then in one cubic meter there would be 2.7 × 10¹⁰ molecules/cm³ × 1,000,000 cm³/m³ = 2.7 × 10¹⁶ molecules/m³.

So, the correct number of molecules per cubic meter at a pressure of one billionth (10⁻⁹) of atmospheric pressure is 2.7 × 10¹⁶ molecules, making the first option the correct answer.