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Chapter 1: Problem 75

A student is given a crucible and asked to prove whether it is made of pure platinum. She first weighs the crucible in air and then weighs it suspended in water (density \(=0.9986 \mathrm{~g} / \mathrm{mL}\) ). The readings are \(860.2 \mathrm{~g}\) and \(820.2 \mathrm{~g},\) respectively. Based on these measurements and given that the density of platinum is \(21.45 \mathrm{~g} / \mathrm{cm}^{3},\) what should her conclusion be? (Hint: An object suspended in a fluid is buoyed up by the mass of the fluid displaced by the object. Neglect the buoyance of air.)

Short Answer

Expert verified
After calculating the density of the crucible, compare the value to the density of platinum. If they are equal, the crucible is made of pure platinum. If they differ, the crucible is not made of pure platinum.

Step by step solution

01

Calculate the Change in Mass

Subtract the apparent mass of the crucible from its real mass to find the change in its mass due to the water. This is given by the equation \( \Delta m = m_{crucible} - m_{apparent, crucible} \). This represents the mass of the water displaced by the crucible.
02

Compute the Volume of the Crucible

Use the mass change and the density of the water to find the volume of the crucible. From the equation \( V_{crucible} = \Delta m / \rho_{water} \), the volume of the crucible can be determined.
03

Calculate the Density of the Crucible

Finally, the density of the crucible can be calculated. The density is given by the ratio of mass to volume. Therefore, using \(\rho_{crucible} = m_{crucible} / V_{crucible}\), the density of the crucible can be computed.
04

Conclude if the Crucible is Made of Pure Platinum

If the density obtained in step 3 matches the density of platinum, then the crucible is made of platinum. If not, it is not made of pure platinum.

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Most popular questions from this chapter

The unit "troy ounce" is often used for precious metals such as gold (Au) and platinum ( \(\mathrm{Pt}\) ). ( 1 troy ounce \(=31.103\) g.) (a) A gold coin weighs 2.41 troy ounces. Calculate its mass in grams. (b) Is a troy ounce heavier or lighter than an ounce? ( \(1 \mathrm{lb}=\) \(160 z ; 1 \mathrm{lb}=453.6 \mathrm{~g} .)\)

Give an example for each of the following terms: (a) matter. (b) substance (c) mixture.

A graduated cylinder is tilled to the \(40.00-\mathrm{mL}\) mark with a mineral oil. The masses of the cylinder before and after the addition of the mineral oil are \(124.966 \mathrm{~g}\) and \(159.446 \mathrm{~g},\) respectively. In a separate experiment, a metal ball bearing of mass \(18.713 \mathrm{~g}\) is placed in the cylinder and the cylinder is again filled to the 40.00 -mL mark with the mineral oil. The combined mass of the ball bearing and mineral oil is 50.952 g. Calculate the density and radius of the ball bearing. [The volume of a sphere of radius \(r\) is $\left.(4 / 3) \pi r^{3} .\right].

Suppose that a new temperature scale has been devised on which the melting point of ethanol \(\left(-117.3^{\circ} \mathrm{C}\right)\) and the boiling point of ethanol \(\left(78.3^{\circ} \mathrm{C}\right)\) are taken as \(0^{\circ} \mathrm{S}\) and \(100^{\circ} \mathrm{S},\) respectively where \(S\) is the symbol for the new temperature scale. Derive an equation relating a reading on this scale to a reading on the Celsius scale. What would this thermometer read at \(25^{\circ} \mathrm{C}\) ?

Measurements show that \(1.0 \mathrm{~g}\) of iron (Fe) contains \(1.1 \times 10^{22}\) Fe atoms. How many Fe atoms are in \(4.9 \mathrm{~g}\) of Fe, which is the total amount of iron in the body of an average adult?
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