Question

An air mattress is filled with 0. 55 moles of air. The air inside the mattress has a temperature of 295 K and a gauge pressure of 3. 5 kilopascals. What is the volume of the air mattress?

Answer 1

49.3 liters

Step-by-step explanation:

To determine the volume of the air mattress, we need to know the equation of state of the air inside the mattress. One commonly used equation of state for an ideal gas is the ideal gas law: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

We can rearrange this equation to solve for volume:

V = nRT/P

Using the given values, we have:

V = (0.55 moles)(8.31 J/mol·K)(295 K)/(3500 Pa)

Converting the pressure from kilopascals to pascals:

V = (0.55 moles)(8.31 J/mol·K)(295 K)/(3500 Pa)

V = (0.55 moles)(8.31 J/mol·K)(295 K)/(3500 N/m^2)

V = 0.55 moles * 8.31 J/mol·K * 295 K / 3500 N/m^2

We can now calculate the volume:

V = 49.3 L

So, the volume of the air mattress is approximately 49.3 liters.