To find the new volume of the gas when the pressure increases to 2.90 atm at the same temperature, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature
First, we need to convert the initial pressure and volume to consistent units. Given:
Initial pressure, P1 = 1.23 atm
Initial volume, V1 = 101 mL
Convert 101 mL to liters by dividing by 1000:
V1 = 101 mL ÷ 1000 = 0.101 L
Now, we can rearrange the ideal gas law equation to find the number of moles of gas (n) at the initial conditions:
n = (P1 * V1) / (R * T)
Since the temperature remains constant, the number of moles (n) is constant for both initial and final states.
Next, we can find the final volume (V2) using the new pressure (P2 = 2.90 atm):
V2 = (n * R * T) / P2
Substitute the initial number of moles calculated earlier into the equation to find the final volume the gas will occupy at 2.90 atm pressure.
