Uranus is much larger than Earth, with a surface area of 8.10 * 1015m2 with an atmosphere of low-density gases: 82.5% H2, 15.2% He, and 2.30% CH4. The acceleration due to gravity is similar to that on Earth, 8.70 m/s2, yet the atmospheric pressure on Uranus is estimated to exceed 1.00 * 108Pa.

Question

Clinton Weeks

Chemistry

20 January, 12:37

Uranus is much larger than Earth, with a surface area of 8.10 * 1015m2 with an atmosphere of low-density gases: 82.5% H2, 15.2% He, and 2.30% CH4. The acceleration due to gravity is similar to that on Earth, 8.70 m/s2, yet the atmospheric pressure on Uranus is estimated to exceed 1.00 * 108Pa.

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Answers (1)

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Kendall Lyons · Answer 1

mass of Uranus: 9.31x10^22 kg

Explanation:

As I stated in the comments, the question in this problem is to calculate the mass of Uranus, given it's conditions.

Now, we have the data of the atmosphere gases, but for calculations, this data is irrelevant.

To calculate the mass of Uranus, we can use the second law of Newton which is:

F = m * a (1)

In this case, the only Force exerting here would be the weight so:

F = m * g (2)

And the force of Uranus, can also be expressed in terms of pressure and Area so:

F = P * S (3)

Now, if we replace (3) in (2) we have:

P * S = m * g

Solving for m:

m = P * S / g (4)

We have all the data, therefore, let's replace it in the above expression to calculate the mass of Uranus:

m = 1x10^8 * 8.1x10^15 / 8.7

m = 9.31x10^22 kg

This is the mass of Uranus