If 3.21mol of a gas occupies 56.2L at 44C and 793torr ,5.29 mol of this gas occupies _______ L under these conditions.
To solve this problem, we can use the ideal gas law equation, which states:
PV = nRT,
where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.
Given information:
- For the first scenario:
- n1 = 3.21 mol,
- V1 = 56.2 L,
- T1 = 44°C = 44 + 273.15 = 317.15 K (temperature in Kelvin),
- P1 = 793 torr.
- We want to find the volume, V2, when n2 = 5.29 mol, under the same conditions (T2 = 317.15 K and P2 = 793 torr).
First, we need to rearrange the ideal gas law equation to solve for V2:
V2 = (n2 * R * T2) / P2.
To use this equation, we need to know the value of the ideal gas constant, R, which is 0.0821 L·atm/(mol·K).
Now we can substitute the values into the equation to find V2:
V2 = (5.29 mol * 0.0821 L·atm/(mol·K) * 317.15 K) / 793 torr.
Before we proceed with the calculations, let's convert torr to atm, as the ideal gas constant is in atm:
1 atm = 760 torr.
So, P2 = 793 torr / 760 torr/atm = 1.0447 atm.
Now we can substitute the values and solve for V2:
V2 = (5.29 * 0.0821 * 317.15) / 1.0447.
By performing this calculation, we find V2 ≈ 129.59 L.
Therefore, 5.29 mol of this gas occupies approximately 129.59 L under the given conditions.
if the conditions are the same temp,pressure, then volume is directly proportional to moles
Volume/56.2 = 5.29/3.21