A balloon contains 3900cm 3 of a gas at a pressure of 101 kPa and a temperature of –9°C. If the balloon is warmed such that the temperature rises to 28°C, what volume will the gas occupy? Assume the pressure remains constant.

Hey, everybody. So let's get started with this problem here. So I've got a balloon. This balloon contains 39 100 centimeters cubed of a gas. The pressure is a 101 kilopascals and the temperature is negative 9 Celsius. So I've got this little balloon like this. Basically, what's happening is I got this this temperature of this balloon is negative 9, but then I'm gonna change it somehow. I'm gonna change it or warm up the balloon such that the temperature rises to 28 degrees Celsius. So basically now I've got this other balloon like this and it's gonna be at 28 Celsius. Now we know we change some of the characteristics of an ideal gas, for example PV or T, then the other variables have to change as a result. So we know we're gonna deal with changing the ideal gas law. So let's go ahead and take a look at our steps here. The first thing we're gonna do is write out this big equation that relates all of the variables for ideal gases. So let's get started. We have p initial, v initial divided by n initial, t initial. This is gonna equal p final, v final divided by n final, t final. Alright. So that's step 1. The next thing we do is we cancel out what the constant variables are. So which ones are gonna remain constant? Well, let's see. Well, the temperature certainly isn't going to remain constant, and we're told that the pressure is going to remain constant. So the pressure is gonna be out, so we're gonna cancel that out. So what about the volume? Well, we can kind of assume or infer from the problem that the volume is going to change. So basically, your changing variables are gonna be volume and temperature. So the one that's kind of constant is gonna be the number of moles in the gas. This kind of makes sense because if you have a balloon like this, right, if nothing is allowed to sort of like, you know, enter in or leave the balloon, then the amount of gas that's inside has to remain constant. Alright. So these are your 2 constant variables. So then what we have to do is just solve for our target variable. What we're really interested in is basically what is the final volume of the gas. So all I have to do is just move the final temperature over to the other side of the equation like this, and really what we have is I can just start plugging in some numbers. Now just be really careful when you do this. There's actually 2 ways to do this. You can leave everything in centimeters cubed first or you can do the conversion. Either way is actually up to you, because we have sort of two sides of an equation. As long as you keep the units the same, it actually should work out and you can convert something in the end. I'm just gonna go ahead and convert this, initially. So my initial volume is 39100. So what I have to do is remember I have to move the decimal place back twice, but three times because I'm dealing with 8 volume. Right? So I have to 123456. Right? So basically this is equal to 0.00 actually, this is gonna be 0039, meters cubed. Right? So what I can do here is 0.0039, and then this is gonna be times the initial or times the final temperature. So the temperature final here is gonna be 28 degrees Celsius. So what I have to do is I have to add 273 to this. So this is gonna be, 301 Kelvin. So that's my T final, 301. Then I have to divide by the initial temperature. The initial temperature is negative 9 Celsius. So this is equal to, let's see, negative 9 +273, and that's equal to 264 Kelvin. So this is my t initial and this is my t final. Alright? So this is gonna be divided by 264. That's gonna give me the final volume and if you work this out here what you're gonna get is 0.0044 meters cubed. Alright? So that's your answer looking through your answer choices. It's answer choice d. So basically what happens here is that we went from an initial volume of 0.0039 to 0.0044. So the volume increased, and that kind of makes some sense because we warmed the gas up from negative 9 to 28. You've warmed the gas, you've added a little bit more energy in it, and if the pressure remains constant, what happens is that the volume has to kind of increase a little bit. Right? So basically the balloon kind of puffed up just a little bit, added a little bit more volume inside. Anyway, so that's it for this one guys.

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A balloon contains 3900cm3 of a gas at a pressure of 101 kPa and a temperature of –9°C. If the balloon is warmed such that the temperature rises to 28°C, what volume will the gas occupy? Assume the pressure remains constant.

다음 시청

A balloon contains 3900cm³ of a gas at a pressure of 101 kPa and a temperature of –9°C. If the balloon is warmed such that the temperature rises to 28°C, what volume will the gas occupy? Assume the pressure remains constant.