$5.$ A propane storage tank with a volume of $10,000$ liters is being taken out of service for maintenance. The tank must be drained of its liquid propane, depressurized to atmospheric pressure, and then inerted with nitrogen prior to opening the tank to air. The temperature is $25\backslash$deg C and the ambient pressure is $1$ atm.

a$.$ Determine the required target fuel concentration in the tank prior to opening the tank.

b$.$ A sweep purge will be used for the inerting procedure. If pure nitrogen is available at a delivery rate of $0\mathrm{.}5$ kg$/$min$,$ what is the minimum time $($in min$)$ required to reduce the fuel concentration to the target value?

c$.$ What is the total amount $($in kg$)$ of nitrogen required to do the job?