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Chapter 1: Problem 66

The density of pure silver is \(10.5 \mathrm{~g} / \mathrm{cm}^{3}\) at \(20^{\circ} \mathrm{C}\). If \(5.25 \mathrm{~g}\) of pure silver pellets is added to a graduated cylinder containing \(11.2 \mathrm{~mL}\) of water, to what volume level will the water in the cylinder rise?

Short Answer

Expert verified
The new volume level of the water in the graduated cylinder when the silver pellets are added to it is \(11.7 \mathrm{~mL}\).

Step by step solution

01

Find the volume of the silver pellets

Using the formula for density, which is density = mass / volume, we can find the volume of the silver pellets. Rearranging the formula to solve for volume gives us volume = mass / density. We know the mass of the silver pellets is \(5.25 \mathrm{~g}\) and the density of pure silver is \(10.5 \mathrm{~g} / \mathrm{cm}^{3}\). Plugging in these values, we can find the volume: Volume = mass / density Volume = \(5.25 \mathrm{~g} / 10.5 \mathrm{~g} / \mathrm{cm}^{3}\) Volume = \(0.5 \mathrm{~cm}^{3}\)
02

Convert volume to milliliters

Since the volume of the water in the graduated cylinder is given in milliliters, we need to convert the volume of the silver pellets from cubic centimeters to milliliters. Knowing that 1 cubic centimeter is equal to 1 milliliter, we can convert the volume of the silver pellets: Volume = \(0.5 \mathrm{~cm}^{3} * \frac{1 \mathrm{~mL}}{1 \mathrm{~cm}^{3}}\) Volume = \(0.5 \mathrm{~mL}\)
03

Find the new volume level of the water

Now that we have the volume of the silver pellets in milliliters, we can determine the new volume level of the water in the graduated cylinder when the silver pellets are added to it. Since the volume of the water was originally \(11.2 \mathrm{~mL}\), we can add the volume of the silver pellets to find the new volume level: New volume level = original volume of water + volume of silver pellets New volume level = \(11.2 \mathrm{~mL} + 0.5 \mathrm{~mL}\) New volume level = \(11.7 \mathrm{~mL}\)
04

State the final answer

The new volume level of the water in the graduated cylinder when the silver pellets are added to it is \(11.7 \mathrm{~mL}\).

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Most popular questions from this chapter

At the Amundsen-Scott South Pole base station in Antarctica, when the temperature is \(-100.0^{\circ} \mathrm{F}\), researchers who live there can join the " 300 Club" by stepping into a sauna heated to \(200.0^{\circ} \mathrm{F}\) then quickly running outside and around the pole that marks the South Pole. What are these temperatures in \({ }^{\circ} \mathrm{C}\) ? What are these temperatures in \(\mathrm{K}\) ? If you measured the temperatures only in \({ }^{\circ} \mathrm{C}\) and \(\mathrm{K}\), can you become a member of the " 300 Club" (that is, is there a 300--degree difference between the temperature extremes when measured in \({ }^{\circ} \mathrm{C}\) and \(\mathrm{K}\) )?

An experiment was performed in which an empty \(100-\mathrm{mL}\) graduated cylinder was weighed. It was weighed once again after it had been filled to the \(10.0-\mathrm{mL}\) mark with dry sand. A \(10-\mathrm{mL}\) pipet was used to transfer \(10.00 \mathrm{~mL}\) of methanol to the cylinder. The sand- methanol mixture was stirred until bubbles no longer emerged from the mixture and the sand looked uniformly wet. The cylinder was then weighed again. Use the data obtained from this experiment (and displayed at the end of this problem) to find the density of the dry sand, the density of methanol, and the density of sand particles. Does the bubbling that occurs when the methanol is added to the dry sand indicate that the sand and methanol are reacting? Mass of cylinder plus wet sand \(\quad 45.2613 \mathrm{~g}\) Mass of cylinder plus dry sand \(\quad 37.3488 \mathrm{~g}\) Mass of empty cylinder \(22.8317 \mathrm{~g}\) Volume of dry sand \(10.0 \mathrm{~mL}\) Volume of sand plus methanol \(\quad 17.6 \mathrm{~mL}\) Volume of methanol \(\quad 10.00 \mathrm{~mL}\)

If a piece of hard white blackboard chalk is heated strongly in a flame, the mass of the piece of chalk will decrease, and eventually the chalk will crumble into a fine white dust. Does this change suggest that the chalk is composed of an element or a compound?

The world record for the hundred meter dash is \(9.74 \mathrm{~s}\). What is the corresponding average speed in units of \(\mathrm{m} / \mathrm{s}, \mathrm{km} / \mathrm{h}, \mathrm{ft} / \mathrm{s}\), and \(\mathrm{mi} / \mathrm{h}\) ? At this speed, how long would it take to run \(1.00 \times 10^{2}\) yards?

Draw a picture showing the markings (graduations) on glassware that would allow you to make each of the following volume measurements of water and explain your answers (the numbers given are as precise as possible). a. \(128.7 \mathrm{~mL}\) b. \(18 \mathrm{~mL}\) c. \(23.45 \mathrm{~mL}\) If you made the measurements of three samples of water and then poured all of the water together in one container, what total volume of water should you report? Support your answer.
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