Question

A basketball has low air pressure. It's initially at a gauge pressure of 6 psi, and you need to inflate it to 7 psi. The volume of the ball is 7000 cm3, and you can approximate that the volume of the ball does not change. SI. What is the initial mass in grams of air in the ball at ambient temperature of 25°C assuming that it is an ideal gas. (Note: convert to absolute values).

Answer 1

To find the initial mass of air in the basketball, we can use the ideal gas law and the given information. Convert the gauge pressure to absolute pressure, convert the volume to liters, calculate the number of moles using the ideal gas law, and then calculate the mass using the molar mass of air.

Step-by-step explanation:

To find the initial mass of air in the basketball, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

First, we need to convert the gauge pressure to absolute pressure. The absolute pressure is the sum of the gauge pressure and the atmospheric pressure. Since the question states that the gauge pressure is 6 psi and the atmospheric pressure is normal, we can assume that it is approximately 14.7 psi. So the absolute pressure is 20.7 psi.

Next, we convert the volume from cm^3 to liters. 7000 cm^3 is equal to 7 liters.

Now we can calculate the number of moles using the ideal gas law: n = PV / RT. Given that R is 0.0821 L·atm / (mol·K) and the temperature is 25°C, which is 298 K, we can substitute the values and solve for n.

Finally, we can calculate the mass using the molar mass of air, which is approximately 28.96 g/mol. The initial mass of air in the basketball is equal to the number of moles multiplied by the molar mass.