The answer is: [D]: platinum .
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Explanation: Given the information provided, we need to find the "density" of the unknown metal; in: "mass per UNIT volume". Then we need to look up the "density" values of EACH of the 4 answer choices (or at least until we get the corresponding density). To be thorough, we still should look up the density of EACH of the metals listed in the answer choices given. We look up these "densities" online, or in a specialty reference guide in university library, for instance.
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First, let us calculate the density of the unknown volume:
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Density, "D", = m / V ; in which: D = density; m = mass; V = volume;
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We are given: mass, "m" = 53.5 g ; and:
Volume, "V" = 2.5 cubic centimeters = 2.5 cm³
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D = 53.5 g / 2.5 cm³ = (53.5 / 2.5) g / cm³ = 21.4 cm³ ;
→ Round to "2 significant figures";
= 21 g/cm³
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We are given 4 (four) answer choices). Let us list EACH of the 4 (four) answer choices and their densities (researched).
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Choice "A" : copper; (Cu) ; density = 8.96 g / cm³ ;
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Choice "B" : iron ; (Fe) ; density = 7.874 g / cm³ ;
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Choice "C": lead; (Pb) ; density = 11.34 g / cm³ ;
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Choice "D": platinum; density = 21.45 g / cm³ ;
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Clearly, Answer choice: [D]: "platinum" is the correct answer; with a density of "21.45 g / cm³ " ;
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Since this value is the closest to our calculated value of
" 21 g/ cm³ "; or even "21.4 g/ cm³ " [our value before rounding down to 2 (two) significant figures].
The densities of the metals in all the other answer choices given are far from this value.
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I hope this explanation has been of some help.