Synthetic diamonds can be manufacated at pressures of 6.00 x 10 in power 4 atm . If we took 2.00 litres of gas at 1.00 atm and compressed it to a pressure of 6.00 x 10 in power 4 atm , what would the volume of that gas be ?
To solve this problem, we can use Boyle's law, which states that the product of pressure and volume for a given amount of gas is constant, as long as temperature remains constant.
Boyle's law equation is expressed as:
P₁V₁ = P₂V₂
where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume.
Given:
Initial pressure (P₁) = 1.00 atm
Initial volume (V₁) = 2.00 L
Final pressure (P₂) = 6.00 x 10⁴ atm
We need to find the final volume (V₂).
Using the Boyle's law equation, we can rearrange it to solve for V₂:
V₂ = (P₁V₁) / P₂
Substituting the given values:
V₂ = (1.00 atm * 2.00 L) / (6.00 x 10⁴ atm)
Now, let's simplify the calculation:
V₂ = (2.00 L) / (6.00 x 10⁴)
To evaluate this expression, divide 2.00 by 6.00 x 10⁴:
V₂ = 3.33 x 10⁻⁵ L
Therefore, when the gas is compressed from 2.00 L at 1.00 atm to a pressure of 6.00 x 10⁴ atm, the final volume of the gas would be approximately 3.33 x 10⁻⁵ L.