/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 66 The density of pure silver is \(... [FREE SOLUTION] | 91影视

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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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