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Answer:
x = 1.00486 m
Explanation:
The complete question is:
" The potential energy between two atoms in a particular molecule has the form U(x) =(2.6)/x^8 −(5.1)/x^4 where the units of x are length and the num- bers 2.6 and 5.1 have appropriate units so that U(x) has units of energy. What is the equilibrium separation of the atoms (that is the distance at which the force between the atoms is zero)? "
Solution:
- The correlation between force F and energy U is given as:
F = - dU / dx
F = - d[(2.6)/x^8 −(5.1)/x^4] / dx
F = 20.8 / x^9 - 20.4 / x^5
- The equilibrium separation distance between atoms is given when Force F is zero:
0 = 20.8 / x^9 - 20.4 / x^5
0 = 20.8 - 20.4*x^4
x^4 = 20.8/20.4
x = ( 20.8/20.4 )^0.25
x = 1.00486 m
A sample of nitrogen gas has a volume of 5.0 ml at a pressure of 1.50 atm. what is the pressure exerted by the gas if the volume increases to 30.0 ml, at constant temperature is 0.25atm.
On constant temperature, the pressure and volume relation become constant before and after the change in quantitities have occurred.
According to Boyle's Law,
P₁V₁ = P₂V₂
where, P₁ is pressure exerted by the gas initially
V₁ is the volume of gas initially
P₂ is pressure exerted by the gas finally
V₂ is the volume of gas finally
Given,
P₁ = 1.5 atm
V₁ = 5 ml
V₂ = 30 ml
P₂ =?
On substituting the given values in the above equation:
P₁V₁ = P₂V₂
1.5 atm × 5 ml = P₂ × 30 ml
P₂ = 0.25 atm
Hence, pressure exerted by the gas is 0.25atm.
Learn more about Boyle's Law here, brainly.com/question/1437490
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