A balloon contains 0.158 mol of gas and has a volume of 2.46 L. If an additional 0.113 mol of gas is added to the balloon (at the same temperature and pressure), what is its final volume?

Video transcript

Welcome back everyone to another video. A balloon contains 0.158 moles of gas and has a volume of 2.46 L. If an additional 0.245 moles of gas is added to the balloon at the same temperature and pressure. What is its final volume? We're given four answer choices. A 6.27 B 13.4 C 2.7 and D 5.69 all given in liters. So let's recall the ideal gas law. We're dealing with a gas here. PV equals NRC. What we know is that pressure and temperature, they are constant, meaning the only variables that are changing are volume and moles. So we can use the avocados law which says that if we rearrange this formula, we get our constants on the right and V divided by N is constant. So that means if we have two conditions, then V one divided by N one should be equal to V two divided by N two. Now let's define our variables. V one, the initial volume is 2.46 L and one, the initial number of moles would be 0.158 moles. Now we don't know the final number of moles and two, but we know that we are adding an additional amount to N one. So let's call it N one plus delta N where delta N is that additional amount of 0.245 moles. So don't be mistaken, the additional amount is not the final number of moles. It's actually an additional amount relative to the initial number of moles. Meaning we can say that our formula becomes V one divided by N one is equal to V two divided by N two which is N one plus delta N. And we're solving for the final volume. So we can say that V two is equal to V one multiplied by N one. Actually, let's make it more clear. V one multiplied by and one plus delta M divided by and one. OK. And now from here, we can make it even neater right? Using basic algebra. We can say that the file formula would be V one, N, one divided by N one is one plus delta M divided by and one. Now let's substitute the given. So V one is 2.46 liters and we multiply that by one plus delta M which is 0.245 moles divided by and one which is the initial number of moles, 0.158 moles. Well, then, so we have our calculation, we are ready to get the final answer, which gives us 6.27 L. And now this corresponds to the answer choice. A that would be it for today. And thank you for watching.