Question

A balloon containing 3.45 x 10²⁶ molecules of hydrogen gas has a volume of 1.55 L. How many molecules of hydrogen gas escaped if the volume decreased at constant temperature and pressure to 0.98 L?

Answer 1

Approximately 1.27 x 10²⁶ molecules of hydrogen gas escaped when the volume decreased from 1.55 L to 0.98 L at constant temperature and pressure.

To find the number of molecules of hydrogen gas that escaped, we can use the relationship between volume and the number of molecules, assuming constant temperature and pressure.

Given:

Initial volume (V₁) = 1.55 L

Initial number of molecules (N₁) = 3.45 x 10²⁶

Final volume (V₂) = 0.98 L

First, we need to calculate the initial number of molecules per liter (N₁/L₁):

N₁/L₁ = 3.45 x 10²⁶ / 1.55 L = 2.23 x 10²⁶ molecules/L

Next, we can calculate the final number of molecules (N₂) using the final volume (V₂):

N₂ = N₁/L₁ x V₂ = (2.23 x 10²⁶ molecules/L) x (0.98 L) = 2.18 x 10²⁶ molecules

To find the number of molecules that escaped, we subtract the final number of molecules from the initial number of molecules:

Number of molecules escaped = N₁ - N₂ = (3.45 x 10²⁶ molecules) - (2.18 x 10²⁶ molecules) = 1.27 x 10²⁶ molecules

Therefore, approximately 1.27 x 10²⁶ molecules of hydrogen gas escaped when the volume decreased from 1.55 L to 0.98 L at constant temperature and pressure.