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What pressure will be required for neon at $30^{\circ} \mathrm{C}$ to have the same density as nitrogen at $20^{\circ} \mathrm{C}$ and 1.0 atm?

$$1.5 \mathrm{atm}$$

Chemistry 101

Chapter 5

Gases

Drexel University

University of Kentucky

Lectures

05:03

In physics, a gas is one of the three major states of matter (the others being liquid and solid). A gas is a fluid that does not support tensile stress, meaning that it is compressible. The word gas is a neologism first used by the early 17th-century Flemish chemist J.B. van Helmont, based on the Greek word ("chaos"), the simplest of all the elemental forms of matter.

04:46

In physics, thermodynamics is the science of energy and its transformations. The three laws of thermodynamics state that energy can be exchanged between physical systems as heat and work; that the total energy of a system can be calculated by adding up all forms of energy in the system; that energy spontaneously flows from being localized to becoming dispersed, spread out, or uniform; and that the entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.

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Given information for the above question, temperature denoted by the non is equal to 30 degree centigrade. Here we convert the degree centigrade into kelvin, so the formula for conversion is 30 degrees. Integrate plus 273 kelvin is equal to 303 kelvin temperature t 4. Nitrogen is equal to 20 degrees centigrade here. We also convert temperature for nitrogen 20 degree centigrade plus 2 ude 73 kelvin is equal to 293 kelvin. So here we have. Pressure of nitrogen is equal to 1.0 at m atmospheric pressure. This is the unit of pressure. Is equal toand we have here ideal gas, constant, constant denoted by r is equal to 0.0821 point. This value is constant, general and gas. Constant are ideal. Gas constant and unit is later atmospheric pressure or kelvin mole. Next, we have the molar mass of mass of mass of men. None denoted by molar mass of non is equal to we have smaller. Mass of neon is 20.18 gram per mole. Next we have nitrogen nitrogen molar mass of nitrogen molar mass is denoted by capital m. In 2 is equal to molar mass of the nitrogen is we have diatomic nitrogen, so 2 into atomic mass of nitrogen is 14.007 gram per mole is equal to inter multiplication to multiply 14 point double 07 gram per mole is equal to 28.014 gram per mole. Now let determine determine the pressure pressure neon pressure of men required required for neon at noon at 30 degrees centigrade to have this same. This same density density denoted by d as nitrogen at 20 degree centigrade here. First, we have to find have to find the density density of nitrogen nitrogen 820 degree centigrade. So we have formula for nitrogen is formula for density of nitrogen and yon is here. We put the formula d density is equal to mass per volume. This is the formula for finding density of nitrogen at 20 degree centigrade. Arnium 30 degree centigrade formula for finding density. We know that is equal to m by molar mass, using the ideal ideal, geslop gesla we get we get here we get by using ideal gisla. We get p v pressure. Volume is equal to n r t number of moles. Here we find number of moles p pressure with its volume is equal to n for a number of moles and r is ideal. Gas constant are general gas. Constant and t is temperature. So we have here p: v, is equal to n, is equal to m by m dot r t, so we also write this formula like b m out of r t is equal to m v is equal to d. So therefore, so therefore d is equal to p m out of r t is equal to. We have p pressure for nitrogen molar mass for nitrogen, divided by r t in toso. We have here by putting by putting values in this formula. We get 1.0 pressure molar mass 28.014 gram per mole divide by we have general gas. Constant is 0.0821 liter 8 t m per kelvin dot mole dot 293 kelvin for nitrogen. So now we calculate these values and get the values density for nitrogen is 1.2 gram per litersince. Both gases gases have the same density, same density. We can calculate the pressure of meon gas using the formula is equal to pressure for neon molar force. Masher neon divide by general gas, constant or temperature for nimis equal to we can rewrite this formula for finding pressure is equal to pressure of or neon is equal to d r t n e divide by molar mass of neon. So, by putting values we have here, p pressure for neon is equal to by putting values in the above formula. 1.2 is density, same density for neon and nitrogen, so we have 1.2 gram per liter density into 0.0821 liter at m atmospheric pressure per kelvin per mole 0.0303 kelvin, its temperature. We have divided by molar. Mass of neon is here 20.18 gram per mole and we have here 1.5 a d m atmospheric pressure or pressure of neon.

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