At a constant pressure of 0.905 atm, a chemical reaction takes place in a cylindrical container with a movable piston having a diameter of 40.0 cm. During the reaction, the height of the piston drops by 65.0 cm. (The volume of a cylinder is V=pr2h,wherehistheheight;1Latm=101.3J.) (a) What is the change in volume in liters during the reaction?

Video transcript

Hello everyone today. We are working with the falling problem. A reaction occurs in a cylindrical container with a movable piston that has a diameter of 55 cm. As the reaction proceeds, the height of the piston rises by 40.5, cm at a constant pressure of .965 atmospheres, calculate the change in volume in leaders for the reaction. We have some useful volume here, which is the volume of the cylinder where h is the height. And then we have what one leader times atmospheres is equal to in jewels. So ultimately we're going to have to calculate the change in our volume. And so we have this formula here. But first we need to solve for our radius. So we need to solve for our radius. So radius is going to be half of the diameter, so diameter divided by two. We have the diameter here which is 55 cm. We simply divide that by two to get 27.5 cm as our radius. So we're gonna hold on to that number for later and now we can solve for our change in our volume Using the equation provided in the question. So we're gonna have pi r squared times our height. Pie is simply going to be a constant times our radius 27.5 centimeters squared and our height Because the piston rose by 40. cm. That is our height. We're ultimately going to get a change in volume of 9.62 times 10 to the 4th cm cute. And we're going to hang on to that number for our last step because we need to solve for volume in leaders and so we have centimeters cubed and so we essentially have to go from centimeters cubed two leaders. So we have our 9.62 times 10 to the 4th cm cubed. And to get to leaders, we're going to have to use a conversion factor. That one militia leader is equal to one centimeter cubed and then we have one millimeter is equal to 10 to the negative third leaders, arguments for milliliters and centimeters cubed cancel out. And we are left with a final answer of 96. L as our final answer. Overall, I hope that this helped and until next time.