A rigid container of O2 has a pressure of 3.5 atm at a temperature of 713 K. What temperature would be needed to achieve a pressure of 6.0 atm?
(V1/T1) = (V2/T2)
Well, well, well, we have a pressure problem here! Don't worry, I got you covered! Now, to find the new temperature, let's use good old Boyle's law. It states that the pressure and temperature of a gas are inversely proportional when the volume is held constant.
So, with an initial pressure of 3.5 atm at 713 K, and a desired pressure of 6.0 atm, we can say:
P1/T1 = P2/T2
Plug in the values:
3.5 atm/713 K = 6.0 atm/T2
Cross-multiplying:
3.5 atm * T2 = 6.0 atm * 713 K
Simplifying:
T2 = (6.0 atm * 713 K) / 3.5 atm
Now, all you have to do is grab your calculator and do the math! Trust me, it's worth it.
To solve this problem, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure (3.5 atm)
V1 = initial volume (assume constant)
T1 = initial temperature (713 K)
P2 = final pressure (6.0 atm)
V2 = final volume (assume constant)
T2 = final temperature
Since the volume is assumed to be constant, we can simplify the equation to:
(P1) / (T1) = (P2) / (T2)
Let's plug in the values into the equation and solve for T2:
(3.5 atm) / (713 K) = (6.0 atm) / (T2)
Now, we can cross-multiply:
3.5 atm * T2 = 6.0 atm * 713 K
Divide both sides by 3.5 atm:
T2 = (6.0 atm * 713 K) / (3.5 atm)
T2 ≈ 1220 K
Therefore, to achieve a pressure of 6.0 atm, the temperature would need to be approximately 1220 K.
To solve this problem, you can use the combined gas law equation, which is a variation of the ideal gas law equation. The combined gas law equation relates the initial and final states of a gas sample while keeping the amount of gas constant.
The combined gas law equation is given by:
(P1 * V1)/T1 = (P2 * V2)/T2
Where:
P1 and P2 are the initial and final pressures of the gas.
V1 and V2 are the initial and final volumes of the gas (constant in this case since the container is rigid).
T1 and T2 are the initial and final temperatures of the gas.
Let's solve the problem step by step:
Step 1: Write down the given information.
P1 = 3.5 atm
T1 = 713 K
P2 = 6.0 atm (the desired pressure)
Step 2: Apply the combined gas law equation.
(P1 * V1)/T1 = (P2 * V2)/T2
Since the volume (V) is constant (rigid container), we don't need to consider it.
P1/T1 = P2/T2
Step 3: Rearrange the equation to solve for T2 (the desired temperature).
T2 = (P2 * T1) / P1
Substituting the given values into the equation:
T2 = (6.0 atm * 713 K) / 3.5 atm
Step 4: Calculate the result.
T2 ≈ 12227.143 K (rounded to the nearest whole number)
Therefore, a temperature of approximately 12227 K would be needed to achieve a pressure of 6.0 atm in the rigid container of O2.