# 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

###### 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:

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

where r = radius.

###### 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

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Density concept. You can view video lessons to learn Density. Or if you need more Density practice, you can also practice Density practice problems.

What is the difficulty of this problem?

Our tutors rated the difficulty ofAn osmium sphere contains 1.289 x 10 23 osmium atoms and has...as low difficulty.

How long does this problem take to solve?

Our expert Chemistry tutor, Jules took 2 minutes and 20 seconds to solve this problem. You can follow their steps in the video explanation above.

What professor is this problem relevant for?

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