# Refractive Index by Pressure/Temperature

by kinogram
Tags: index, refractive
 P: 24 The refractive index of H2 = 1.0001594 under the following conditions : P = 101325 Pa T = 273.15 K I cannot find any source for the refractive index of gases under any other conditions 3 Questions : a. What is the pressure gradient for the refractive index? b. What is the thermal gradient for the refractive index? c. Is there a formula for calculating the refractive index based on the Individual Gas Constant? Thanks!
 Sci Advisor P: 3,633 Sounds like a thread apt for the homework forum.
 P: 24 It's an engineering problem - in need of a solution The refractive index should be directly proportional to pressure where half the pressure = half the refractive index In liquids, I believe the refractive index thermal gradient is around 0.000045 / K where the refractive index (and density) increases as temperature decreases, but I don't think this gradient applies to gases. I found the equation for refractive index below : Attached Thumbnails
P: 3,633
Refractive Index by Pressure/Temperature

 Quote by kinogram The refractive index should be directly proportional to pressure where half the pressure = half the refractive index
Only at constant temperature. In a gas, the refractive index is proportional to the concentration of the gas.
Do you know a relationship between concentration and p and T for dilute gasses?
P: 24
 Only at constant temperature. In a gas, the refractive index is proportional to the concentration of the gas. Do you know a relationship between concentration and p and T for dilute gasses?
I assume you mean the molar concentration per m³

calculated through the ideal gas equation.

$PV = nRT$

For example, we take the refractive index of H2 at 101325 Pa and 273.15 K
which = 1.0001594

The individual gas constant for H2 = 4124 J / kg K

Therefore, using the ideal gas equation, 1 m² of H2 at 101325 Pa and 273.15 K
has a concentration of 0.089949 mol

multiplying the molar concentration by the Avogadro constant - 6.02214129 x 1023

we have a density of 5416861 x 1022 H2 molecules / m³

with the temperature remaining constant, if we reduce the pressure by 2.0265 x 10-22

at 5 x 10-18 Pa and 273.15 K

the refractive index of H2 then = 4.9354 x 10-23

again, using the ideal gas equation, 1 m² of H2 at 5 x 10-18 Pa and 273.15 K
has a concentration of 4.43864225 x 10-24 mol

multiplying the molar concentration by the Avogadro constant

we now have a density of H2 = 2 (.673) molecules / m³

So, we now have an H2 concentration of 4.43864225 x 10-24 mol / m³

and a refractive index of 4.9354 x 10-23

so, if we multiply 2.673 by the temperature difference between 273.15 K and 2.7 K (101.166..)

we have a molar concentration of 4.483455 x 10-22

and a density of 270 H2 molecules per m³

the refractive index increases as temperature decreases
how then do we calculate the refractive index of H2 at 2.7 K ?

.
 Sci Advisor P: 3,633 Huh, you said nothing about being interested in 2.7 K and extremely low pressures. What's this, interstellar vacuum? Maybe you could explain in more detail what you are really trying to do.
P: 24
 Huh, you said nothing about being interested in 2.7 K and extremely low pressures. What's this, interstellar vacuum? Maybe you could explain in more detail what you are really trying to do.
I'm trying to calculate the refractive index of molecular hydrogen (H2) at a given temperature

for example 1% of the 273.15 K baseline temperature = 2.7 K

or we can take 10% of 273.15 K, 27 K as an example.

The melting point of H2 is typically listed as 13.95 K
however the concentration at this melting point is not specified.

The melting point of H2 increases with concentration.

Melting and boiling points are a function of the intermolecular forces (van der Waals forces).

For molecular H2 the only intermolecular forces are London dispersion forces,
and London dispersion forces depend on the polarizability of the molecule.

The greater the number of electrons per volume
the greater the strength of the London dispersion forces.

So, at an extremely low molar concentration of 4.483455 x 10-22 mol / m³
the melting point should be below 2.7 K

In fact below a critical concentration, H2 as a solid should not even be possible.

However, to simplify the problem, we can take 27 K as a temperature

and a molar concentration of 4.49 x 10-23 mol / m³

is there an equation for calculating the refractive index based on concentration alone?

.
 P: 24 actually, the real question is.. does anyone here know the equation for calculating refractive index based on molar comcentration? .
 P: 24 So, I finally got my answer from a chemist : The temperature is irrelevant to a specific quantitative concentration. Concentration itself is a coefficient of temperature and pressure, however once the concentration is defined - that's all we need to know. we can pack up the tents and go home. The refractive index of H2 at a molar concentration of 4.483455 x 10-22 mol / m³ = 4.9354 x 10-23 .
 Sci Advisor P: 3,633 No, the refractive index will be very nearly 1. If the index 1 specifies the standard state and the index 2 the actual state you are interested in then: ##(n_2-1)/(n_1-1)=(p_2T_1)/(p_1T_2)##
P: 24
 No, the refractive index will be very nearly 1. If the index 1 specifies the standard state and the index 2 the actual state you are interested in then: $(n2−1)/(n1−1)=(p2/T1)/(p1T2/)$

Let's check..

p1 = 101325
p2 = 5 x 10-18

T1 = 273.15
T2 = 2.7

(p2T1) = 0.00000000000000136575
(p1T2) = 273577.5

(p2T1) / (p1T2) = 4.992186857471831565 x 10-21

it doesn't quite add up to 1

but the result is 101.15060293941385835182181384441 x the previous result

and if we multiply T2 by this factor we have 273.1066

which would suggest that we are simply multiplying the previous result by (T1/T2)

.
P: 3,633
 Quote by kinogram it doesn't quite add up to 1.
I don't see why it should. Seriously, I gave you a complete formula simply enough to calculate your index of refraction. Solving for n2 should be no problem for someone who wants to do an engineering project with hydrogen at 2.7 K.
P: 24
 I don't see why it should. Seriously, I gave you a complete formula simply enough to calculate your index of refraction.

Of course, I was only responding to your previous reply

 No, the refractive index will be very nearly 1

I assumed you meant that the refractive index should be very nearly 1

in order to achieve a target refractive index, we first reduce the pressure at a constant temperature
until we reach the target, then we reduce the temperature to T2,
which increases the refractive index so we compensate by reducing the pressure again - using the equation
remaining at T2, and we end up with the target refractive index and temperature.

simple

Your equation is exactly what I needed.. Thanks!

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