You are using water to dilute small amounts of chemicals in the laboratory, drop by drop. How many drops of water are in a 1.0-L bottle?

Video transcript

Hey everybody. Today, we're being asked to determine how many drops of dishwashing liquid are in a 1.5 liter bottle estimating that the diameter of a singular drop will be two. The diameter is equal to 2 mm And the volume of the bottle is 1.5 l 1.5 L. So the first thing we need to do is determine because we need to find out the volume of a single drop in order to find out how many drops will therefore be in a bottle with a volume of 1.5 L. So assuming that the drop takes a spherical shape the volume of the sphere is 4/3 multiplied by pi r cubed. When converting this in terms or when thinking of this in terms of diameter this becomes 1/6 multiplied by pi D. Cute. So the value or the Volume of a singular drop of soap with a diameter of 2 mm, 1 drop is equal to 1 6th multiplied by pi one supplied by two. Cute. Which gives us an answer of 4. m mm. Sorry, cute. However, we need to convert this value this volume into leaders because our volume given of the bottle is in leaders and we need those units to be the same in order to carry out our calculations. So we're gonna go from millimeter cute. Oops cubed. Two leaders. And to do this, we start with our 4.1888 millimeter cubed. We know we can recall rather that we have millimeters for every one m so one m to 1000 m but we're dealing with meters or millimeters cubed. So we put that entire term and cubit That will allow us to cancel out these values. But remember both terms do get raised to the power of three M. Just not including that for the sake of space to say space on the paper. But keep that in mind. We also need to remember that 1000 liters of liquid can be present within a one m cubed volume within a space of one m cubed. So we can say 1000 L is present in a one m cubed space. So this will allow me to cancel that meter cubed as well. And carrying out our calculations, this would be 4.111888. The power of three or millimeters cube. Sorry, Divided by 1000 to the power of three all multiplied by 1000 here. And we will end up with an answer of 4.1888 times to the negative six liters per drop. We're not done though. Now we need to figure out how many Dropth would be present within the volume of 1.5 L in the soap bottle. This however is really easy to do. We take the volume of our soap bottle or 1. leaders and we divide That value by the volume. We just got. So it's 4. Times 10 to the negative, 6th leaders per drop. So leaders will cancel out and drops will move up to this top and we'll be left with a final answer. A final answer Of 3000 or sorry. 358,358, 97.78 or approximately 358,098 drops in one bottle of soap. This corresponds to answer choice. A So within one 1.5 L bottle of dishwashing soap, if a single drop has a diameter of two, there will be 300 or 58,098 drops of soap within the bottle. I hope this helps. And I look forward to seeing you all in the next one.