How to Calculate the Amount of Air Inside a Spherical Balloon

Spherical balloon diameter of 50.0 cm, absolute pressure inside is 1.25 atm, temperature is 22.0°C

Final answer: To calculate the amount of air inside a spherical balloon with specified measurements, it would involve using the Ideal Gas Laws. The formula is PV = nRT, where the Pressure (P) is 1.25 atm, Volume (V) can be calculated by the balloon's given diameter, n is the variable we are solving (number of moles), R is the gas constant, and T is the temperature in Kelvin.

Explanation:

The student's question pertains to the principles of gas laws in Physics. Given that we know the spherical balloon's diameter to be 50.0 cm, the absolute pressure inside is 1.25 atm, and the temperature is 22.0°C, we can use the Ideal Gas Law to calculate the quantity of air inside the balloon.

The Ideal Gas Law states that PV = nRT where P represents pressure, V is volume, n denotes the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin. First, we convert the temperature from Celsius to Kelvin which will equal to 295K (22°C + 273). Then the volume of the balloon could be calculated utilizing the formula of sphere volume V = ⁴⁄₃ π r³ where r or radius is half of the diameter or 25.0 cm (50.0/2), which equals to about 65450 cm³ or 65450 x 10^-6 m³. As we now know that the absolute pressure is 1.25 atm, we convert this to Pascal (Pa) because the gas constant R's usual units are J/(mol*K): 1.25 atm = 1.25 * 101300 = 126625 Pa.

Plugging these values into the Ideal Gas Law, we can solve for n: n = PV/RT. This will yield the amount of air inside the balloon in moles.