I need help on these last three problems on my Hw.
1. A 10.0 L sample of gas at 3.00 degrees Celsius is cooled at a constant pressure until it reaches 1/2 of its original volume. At what temperature in K will this volume be reached? (Charles law)
2. 994 mLof gas is collected at STP. At what temperature (in kelvin) will the volume be 590 mL if the pressure remains constant? (Charles law)
3. 22.4 L of gas fills a container at STP (what does STP mean?) If the volume remains constant and the gas is heated to 350 K, what is the new pressure? (In arm) (gay-lussacs law)
1. (V1/T1) = (V2/T2)
What throws students on this kind of problem is that they don't give an initial volume and you must use that and what that volume changes to. The easy way to do these is to assume an initial volume for V1 (any convenient number will do), then take 1/2 that for V2. Then just plug into the equation.
2. Do you know what STP means. Temperature of 273 and pressure of 1 atm. Use same equation as in 1.
3. Now that you know what STP is use (P1/T1) = (P2/T2). You don't need to worry about the 22.4 L (v1 or v2) since that doesn't change.
Use
Sure, I can help you with these three problems. Let's go through each one step by step.
1. To solve this problem using Charles' Law, we need to know the relationship between volume and temperature of a gas at a constant pressure. Charles' Law states that the volume of a gas is directly proportional to its temperature in Kelvin.
We are given that the initial volume (V1) is 10.0 L and the initial temperature (T1) is 3.00 degrees Celsius. To convert this temperature to Kelvin, we need to add 273.15 to it. So, T1 = 3.00 + 273.15 = 276.15 K.
Next, we are told that the gas is cooled at a constant pressure until it reaches 1/2 of its original volume. So, the final volume (V2) is (1/2) * V1. Plugging in the values, we have V2 = (1/2) * 10.0 L = 5.0 L.
Now, we can set up the proportion V1 / T1 = V2 / T2, where T2 is the final temperature we want to find.
Substituting the values, we have:
10.0 L / 276.15 K = 5.0 L / T2
Cross-multiplying, we get:
10.0 L * T2 = 5.0 L * 276.15 K
Dividing both sides by 5.0 L, we get:
T2 = (5.0 L * 276.15 K) / 10.0 L
Simplifying, we find that:
T2 = 1380.75 K
Therefore, the temperature at which the gas reaches a volume of 5.0 L is 1380.75 K.
2. This problem also involves Charles' Law. Given that the initial volume (V1) is 994 mL and the final volume (V2) is 590 mL, we are asked to find the temperature in Kelvin (T2) at which this volume change occurs.
At constant pressure, we can set up the same proportion as before: V1 / T1 = V2 / T2.
Substituting the values, we have:
994 mL / T1 = 590 mL / T2
Since the pressure remains constant, we don't need to convert the volumes to liters. We can leave them in milliliters.
To solve for T2, we can cross-multiply and then divide:
994 mL * T2 = 590 mL * T1
T2 = (590 mL * T1) / 994 mL
Now, we know that at Standard Temperature and Pressure (STP), the temperature is 273.15 K. So, we can substitute that value for T1:
T2 = (590 mL * 273.15 K) / 994 mL
Simplifying, we find that:
T2 = 161.65 K
Therefore, when the volume of the gas is reduced from 994 mL to 590 mL at constant pressure, the temperature will be 161.65 K.
3. STP stands for Standard Temperature and Pressure. It is a set of conditions used as a reference point for gas calculations. At STP, the temperature is 273.15 K (0 degrees Celsius) and the pressure is 1 atmosphere (atm).
In this problem, we have a fixed volume of 22.4 L at STP. We are asked to find the new pressure when the gas is heated to 350 K.
This problem involves Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its absolute temperature, assuming the volume remains constant.
We know the initial temperature (T1) is 273.15 K and the final temperature (T2) is 350 K. Let's call the initial pressure P1 and the final pressure P2.
Using the proportionality relationship, we can set up the equation:
P1 / T1 = P2 / T2
Substituting the values, we have:
P1 / 273.15 K = P2 / 350 K
Rearranging the equation, we can solve for P2:
P2 = (P1 * 350 K) / 273.15 K
Since the initial pressure was not given in the problem, we cannot determine the exact value of P2 without it. However, you can substitute the known value for P1 if it was provided in the question.
I hope this helps you understand how to approach these problems.