# Problem: An osmium sphere contains 1.289 x 10 23 osmium atoms and has a radius 0.755 cm. The molar mass of osmium is 190.23 g•mol-1. What is the density of osmium? Recall that the volume of a sphere is given by the formula: 4/3 π r 3a. 22.6 g/cm 3 b. 6.24 g/cm 3c. 1.80 g/cm 3d. 0.822 g/cm 3

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###### FREE Expert Solution

We’re being asked to determine the density of osmium (Os) given that an osmium sphere containing 1.2989 × 1027 atoms has a radius of 0.755 cm.

Recall that density is the ratio of the mass and volume of an object:

$\overline{){\mathbf{density}}{\mathbf{=}}\frac{\mathbf{mass}}{\mathbf{volume}}}$

Also, the volume of a sphere is given by:

$\overline{){\mathbf{V}}{\mathbf{=}}\frac{\mathbf{4}}{\mathbf{3}}{{\mathbf{\pi r}}}^{{\mathbf{3}}}}$ ###### Problem Details

An osmium sphere contains 1.289 x 10 23 osmium atoms and has a radius 0.755 cm. The molar mass of osmium is 190.23 g•mol-1. What is the density of osmium? Recall that the volume of a sphere is given by the formula: 4/3 π r 3

a. 22.6 g/cm 3

b. 6.24 g/cm 3

c. 1.80 g/cm 3

d. 0.822 g/cm 3

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Based on our data, we think this problem is relevant for Professor Myers' class at NAU.