A balloon vendor at a street fair is using a tank of helium to fill her balloons. The tank has a volume of 124.0 L and a pressure of 104.0 atm at 24.0 °C. After a while she notices that the valve has not been closed properly. The pressure had dropped to 94.0 atm. (The tank is still at 24.0 °C.)How many moles of gas has she lost?

She lost 50.88 moles

Explanation:

Step 1: Data given

The volume of the tank = 124.0 L

The initial pressure = 104.0 atm

The temperature = 24.0 °C = 297 K

The pressure drops to 94.0 atm

The temperature stays constant at 297 K

Step 2: Calculate the initial number of moles

p*V = n*R*T

n = (p*V)/(R*T)

⇒with p = the initial pressure = 104.0 atm

⇒with V = the initial volume = 124.0 L

⇒with n = the initial number of moles = TO BE DETERMINED

⇒with R = the gas constant = 0.08206 L*atm/mol*K

⇒ with T = the temperature= 297 K

n = (104.0*124.0)/(0.08206*297)

n = 529.14 moles

Step 3: Calculate final number of moles

p*V = n*R*T

n = (p*V)/(R*T)

⇒with p = the initial pressure = 94.0 atm

⇒with V = the initial volume = 124.0 L

⇒with n = the initial number of moles = TO BE DETERMINED

⇒with R = the gas constant = 0.08206 L*atm/mol*K

⇒ with T = the temperature= 297 K

n = (94.0*124.0)/(0.08206*297)

n = 478.26 moles

Step 4: Calculate the difference of moles

529.14 moles - 478.26 moles = 50.88 moles

She lost 50.88 moles