A sample of an ideal gas has a volume of 3.35 L at 14.00 °C and 1.40 atm. What is the volume of the gas at 21.60 °C and 0.993 atm?
Too easy to be lost.
(P1V1/T1) = (P2V2/T2)
Remember T must be in kelvin.
thank you drbob222
To solve this problem, we can use the combined gas law equation, which relates the initial and final states of a gas sample. The equation is given as:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 and P2 are the initial and final pressures,
V1 and V2 are the initial and final volumes,
and T1 and T2 are the initial and final temperatures.
Given:
P1 = 1.40 atm
V1 = 3.35 L
T1 = 14.00 °C = 14.00 + 273.15 K (convert to Kelvin)
Now, we need to find P2 and V2 using the given temperature T2 = 21.60 °C = 21.60 + 273.15 K.
First, let's convert the initial temperature to Kelvin:
T1 = 14.00 + 273.15 = 287.15 K
Now we can substitute the given values into the combined gas law equation:
(1.40 atm * 3.35 L) / (287.15 K) = (P2 * V2) / (294.75 K)
To find V2, we rearrange the equation and plug in the remaining values:
(1.40 atm * 3.35 L * 294.75 K) / (287.15 K) = P2 * V2
Now we can solve for V2:
V2 = (1.40 atm * 3.35 L * 294.75 K) / (287.15 K * P2)
Finally, we need to find the value of P2. We can use the ideal gas law equation, which states:
P * V = n * R * T
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 in Kelvin.
Since we are dealing with an ideal gas, the number of moles of gas (n) and the gas constant (R) remain constant.
Now let's substitute the given values into the ideal gas law equation to find P2:
P2 * V2 = P1 * V1 * (T2 / T1)
Now we can solve for P2:
P2 = (P1 * V1 * T2) / (V2 * T1)
Substitute the given values:
P2 = (1.40 atm * 3.35 L * 294.75 K) / (V2 * 287.15 K)
Now, plug in the expression for V2 obtained earlier and solve for P2:
P2 = (1.40 atm * 3.35 L * 294.75 K) / ((1.40 atm * 3.35 L * 294.75 K) / (287.15 K * P2) * 287.15 K)
After simplifying the equation, you can solve for P2. Once you have the value of P2, substitute it back into the equation for V2 and solve for V2.