Question

5. Methane is stored in a 120 L tank at - 15 °C and a pressure of 135 atm. The gas is used to fuel a furnace. The furnace consumes on average 550 L of methane a day. How long will this supply of methane last if it is burned at 400 °C at a pressure of 95 kPa?

Answer 1

To calculate how long the supply of methane will last, we need to determine the amount of methane consumed per day. The furnace consumes 550 L per day. Using the ideal gas law, we calculate the number of moles of methane being consumed each day. By dividing the number of moles by the consumption rate, we find that the supply of methane will last approximately 3.9 hours.

Step-by-step explanation:

To calculate how long the supply of methane will last, we need to determine the amount of methane consumed per day. The furnace consumes 550 L per day. We can then use the ideal gas law to calculate the number of moles of methane being consumed each day:

Using the equation PV = nRT, we can rearrange it as n = PV / RT, where n is the number of moles, P is the pressure, V is the volume, R is the gas constant, and T is the temperature. We need to convert the temperature from Celsius to Kelvin by adding 273.15 to it. Plugging the values into the equation, we get:

n = (550 L)(95 kPa) / (8.314 L·kPa/(mol·K))(400 °C + 273.15 K)

n ≈ 88.75 mol

Now, we can calculate how long the supply of methane will last by dividing the number of moles by the consumption rate:

Time = Number of moles / Consumption rate

= 88.75 mol / 550 L per day

= 0.161 days or approximately 3.9 hours.