Final answer:
To find the number of moles of argon in the cylinder, we use the ideal gas law with the given volume, pressure, and converted temperature to calculate approximately 11.87 moles.
Step-by-step explanation:
To calculate the number of moles of argon in a cylinder given its volume, pressure, and temperature, we will use the ideal gas law, which is PV = nRT. To begin the calculation, we should first convert all measurements to appropriate SI units. The temperature in degrees Celsius must be converted to Kelvin by adding 273.15:
T(K) = 1997 °C + 273.15 = 2270.15 K
The volume is already in liters, and the pressure is in atmospheres, which are acceptable units for using the ideal gas constant R = 0.0821 L·atm/(mol·K). Now we can rearrange the ideal gas law to solve for the number of moles (n):
n = PV / RT
Substitute the known values into this equation:
n = (28.4 atm × 70.0 L) / (0.0821 L·atm/(mol·K) × 2270.15 K)
Calculate the number of moles:
n ≈ 11.87 mol
Therefore, there are approximately 11.87 moles of argon in the cylinder.