you have four metal samples, each with a different volume. the volume of each metal sample, the density of…

you have four metal samples, each with a different volume. the volume of each metal sample, the density of the metal, price per gram are shown in the table. metal volume of sample (cm³) density (g/cm³) price per gram cobalt 500.0 8.90 $0.0705 silver 50.0 10.5 $0.743 platinum 0.500 21.5 $31.70 gold 0.250 19.3 $58.78 which sample of metal is most valuable? 500.0 cm³ of cobalt 0.500 cm³ of platinum 0.250 cm³ of gold 50.0 cm³ of silver

Answer

Explanation:

Step1: Recall density - mass formula

$m=\rho V$ (where $m$ is mass, $\rho$ is density, $V$ is volume)

Step2: Calculate mass of cobalt

$m_{cobalt}=\rho_{cobalt}V_{cobalt}=8.90\ g/cm^{3}\times500.0\ cm^{3}=4450\ g$

Step3: Calculate value of cobalt

$V_{cobalt - value}=m_{cobalt}\times price_{per - gram}=4450\ g\times0.0705\ $/g = 4450×0.0705 = 313.725$

Step4: Calculate mass of silver

$m_{silver}=\rho_{silver}V_{silver}=10.5\ g/cm^{3}\times50.0\ cm^{3}=525\ g$

Step5: Calculate value of silver

$V_{silver - value}=m_{silver}\times price_{per - gram}=525\ g\times0.743\ $/g=525×0.743 = 390.075$

Step6: Calculate mass of platinum

$m_{platinum}=\rho_{platinum}V_{platinum}=21.5\ g/cm^{3}\times0.500\ cm^{3}=10.75\ g$

Step7: Calculate value of platinum

$V_{platinum - value}=m_{platinum}\times price_{per - gram}=10.75\ g\times31.70\ $/g = 10.75×31.70=340.775$

Step8: Calculate mass of gold

$m_{gold}=\rho_{gold}V_{gold}=19.3\ g/cm^{3}\times0.250\ cm^{3}=4.825\ g$

Step9: Calculate value of gold

$V_{gold - value}=m_{gold}\times price_{per - gram}=4.825\ g\times58.78\ $/g=4.825×58.78 = 283.4035$

Answer:

0.500 $cm^{3}$ of platinum