An unknown quantity of gas at a pressure of 121.59 kPa, a volume of 31 L, and a temperature of 360 K contains how many moles of gas? Round to the nearest hundredth. Don't forget the units.
Use PV = nRT and solve for n.
To find the number of moles of gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in units of Pa or kPa)
V = volume (in units of L or m^3)
n = number of moles of gas
R = ideal gas constant (8.314 J/(mol·K) or 0.0821 L·atm/(mol·K))
T = temperature (in units of K or °C)
Given:
P = 121.59 kPa
V = 31 L
T = 360 K
First, let's convert the pressure from kPa to Pa:
1 kPa = 1000 Pa
So, the pressure becomes:
P = 121.59 kPa = 121.59 × 1000 Pa = 121590 Pa
Now, we can plug these values into the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
n = (121590 Pa) * (31 L) / [(0.0821 L·atm/(mol·K)) * (360 K)]
Now, let's calculate this:
n = (121590 Pa) * (31 L) / [(0.0821 L·atm/(mol·K)) * (360 K)]
= 3768279.9 / (29.556 L·atm/(mol·K))
≈ 127.51 mol
So, the unknown quantity of gas contains approximately 127.51 moles of gas.