5. A student has the following data: V1 = 822 mL, T1 = 75°C and T2 = -25°C. He calculates V2 and gets -274 mL is this value correct? Explain why or why not.
V1/T1=V2/T2
75+273.15=348.15
-25+273.15=248.15
822/348.15=v2/248.15=586
No, it is not correct because your final answer cannot be a negative answer. :)
Oh my, it seems like the student has stumbled upon the magical land of negative volumes! You see, in the real world, we usually don't get negative volumes. Negative volumes are like the unicorn of the scientific world, extremely rare and quite mythical.
In this case, it looks like the student might have made a mistake somewhere along the way. When dealing with temperature and volume changes, we usually use the equation V1/T1 = V2/T2. Using this equation, we can solve for V2.
Let's plug in the given values: V1 = 822 mL, T1 = 75°C, and T2 = -25°C.
Applying the equation, we have 822 mL / 75°C = V2 / -25°C.
Now let's do some math:
(822 mL * -25°C) / 75°C = V2
-274 mL = V2
Uh-oh, it looks like the student did get -274 mL as the value for V2. But, unfortunately, that's not correct. Negative volumes just don't exist in our world.
So, dear student, you may want to go back and double-check your calculations. Maybe there's a small error hiding in there somewhere. Don't worry, even the best scientists make mistakes sometimes!
To determine if the value of -274 mL for V2 is correct, we need to calculate it using the given data and relevant formula.
The formula that relates initial volume (V1), initial temperature (T1), and final temperature (T2), assuming constant pressure, is:
V2 = (V1 * (T2 + 273.15)) / (T1 + 273.15)
Given data:
V1 = 822 mL
T1 = 75°C
T2 = -25°C
Let's calculate V2 using the formula:
V2 = (822 mL * (-25°C + 273.15)) / (75°C + 273.15)
V2 = (822 mL * 248.15 K) / 348.15 K
V2 ≈ 587.453 mL
Therefore, the value of -274 mL is not correct for V2. The correct value for V2 is approximately 587.453 mL.
To determine if the student's calculation of V2 is correct, we need to use the ideal gas law equation:
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 in Kelvin.
Given:
V1 = 822 mL
T1 = 75°C
T2 = -25°C
To start, we need to convert temperatures from Celsius to Kelvin. The conversion is done by adding 273.15 to the Celsius temperature.
T1 = 75°C + 273.15 = 348.15 K
T2 = -25°C + 273.15 = 248.15 K
Now, the student can set up a ratio using the initial and final states of the gas:
(V1 / T1) = (V2 / T2)
Plugging in the values we have:
(822 mL / 348.15 K) = (V2 / 248.15 K)
To find V2, we need to solve for it:
Cross multiplying:
822 mL * 248.15 K = V2 * 348.15 K
203673.3 mL * K = V2 * 348.15 K
Cancelling out the Kelvin units:
203673.3 mL = V2 * 348.15
To isolate V2, we divide both sides by 348.15:
V2 = 203673.3 mL / 348.15
V2 ≈ 584.9 mL
From the calculation, we find that V2 is approximately 584.9 mL, not -274 mL as the student had calculated. Therefore, the student's value of -274 mL is incorrect.
It is important to note that volume cannot have a negative value in this context. The negative sign in the student's calculation may have come from a mathematical error or a sign convention mistake.