
(a)
Interpretation:
The pressure halfway to the center of the sun assuming that the interior consists of ionized hydrogen atoms at the temperature of
Concept introduction:
Ideal gas equation:
According to kinetic theory of gas the ideal gas is the one having almost negligible volume, no attractive or repulsive force working between the molecules. The molecules are randomly moving and colliding with each other having elastic collisions.
Ideal gas equation can be represented as,
Where,
(a)

Answer to Problem 1.2PR
Pressure in midway of sun is
Explanation of Solution
Given that the temperature in the sun is
It has been assumed that the interior of the sun is filled with the ionized hydrogen atom.
Ideal gas equation,
It can also be written as,
The number of molecules of gas can be represented as,
Now the mass of the ionized hydrogen atom is,
Hence the ideal gas equation can be written as,
For, ionized hydrogen atom,
Now putting all the values in the ideal gas equation,
Hence pressure in midway of sun is
(b)
Interpretation:
The pressure of the plasma is related to its kinetic energy density by
Concept introduction:
Kinetic energy density:
Kinetic energy of the gas molecules is the energy that occurs due to the random motion of the gas molecules.
It can be expressed as,
Kinetic energy of the molecules in a region divided by the volume of that region is the kinetic energy density of the molecules of that region.
Equipartition of energy:
The equipartition theorem shows that in thermal equilibrium any degree of freedom which appears only quadratically in the energy has an average energy of
(b)

Explanation of Solution
According to the equipartition theorem it can be predicted that the monoatomic ideal gas has an average kinetic energy of
Hence it can be concluded that kinetic energy,
From this it can be concluded that,
Now from part (a) the ideal gas equation,
Now combining the above two equations,
Thus it can be shown that
(c)
Interpretation:
Kinetic energy density half way to the center of the sun has to be calculated.
Concept introduction:
Ideal gas equation:
According to kinetic theory of gas the ideal gas is the one having almost negligible volume, no attractive or repulsive force working between the molecules. The molecules are randomly moving and colliding with each other having elastic collisions.
Ideal gas equation can be represented as,
Where,
Kinetic energy density:
Kinetic energy of the gas molecules is the energy that occurs due to the random motion of the gas molecules.
It can be expressed as,
Kinetic energy of the molecules in a region divided by the volume of that region is the kinetic energy density of the molecules of that region.
(c)

Answer to Problem 1.2PR
The sun has kinetic energy density
Explanation of Solution
Pressure to the half way to the center of the sun is
From part (b) relation between the pressure and kinetic energy density obtained is,
Now, putting the value of pressure in this equation,
At
Hence at
Hence
Hence the sun has much more energy density.
Hence the sun has kinetic energy density
(d)
Interpretation:
The pressure halfway to the center of the red giant assuming that the interior consists of fully ionized carbon atoms at the temperature of
Concept introduction:
Ideal gas equation:
According to kinetic theory of gas the ideal gas is the one having almost negligible volume, no attractive or repulsive force working between the molecules. The molecules are randomly moving and colliding with each other having elastic collisions.
Ideal gas equation can be represented as,
Where,
(d)

Answer to Problem 1.2PR
The pressure in midway of red giant is
Explanation of Solution
Given that the temperature at the halfway of the center of the red giant is
The red giant is filled with fully ionized carbon atom.
Ideal gas equation,
It can also be written as,
The number of molecules of gas can be represented as,
Now the mass of the fully ionized carbon atom is,
Hence the ideal gas equation can be written as,
For, fully ionized carbon atom,
Now putting all the values in the ideal gas equation,
Hence pressure in midway of red giant is
(e)
Interpretation:
The pressure halfway to the center of the red giant assuming that the interior consists of neutral carbon atoms at the temperature of
Concept introduction:
Ideal gas equation:
According to kinetic theory of gas the ideal gas is the one having almost negligible volume, no attractive or repulsive force working between the molecules. The molecules are randomly moving and colliding with each other having elastic collisions.
Ideal gas equation can be represented as,
Where,
(e)

Answer to Problem 1.2PR
The pressure in midway of red giant is
Explanation of Solution
Given that the temperature at the halfway of the center of the red giant is
The red giant is filled with neutral carbon atom.
Ideal gas equation,
It can also be written as,
The number of molecules of gas can be represented as,
Now the mass of the fully ionized carbon atom is,
Hence the ideal gas equation can be written as,
For, neutral carbon atom,
Now putting all the values in the ideal gas equation,
Hence pressure in midway of red giant is
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Chapter 1 Solutions
Elements Of Physical Chemistry
- 111 Carbonyl Chem Choosing reagants for a Wittig reaction What would be the best choices for the missing reagents 1 and 3 in this synthesis? 1. PPh3 3 1 2 2. n-BuLi • Draw the missing reagents in the drawing area below. You can draw them in any arrangement you like. Do not draw the missing reagent 2. If you draw 1 correctly, we'll know what it is. • Note: if one of your reagents needs to contain a halogen, use bromine. Explanation Check Click and drag to start drawing a structure. × ©2025 McGraw Hill LLC. All Rights Reserved. Terms of Usearrow_forwardA student proposes the transformation below in one step of an organic synthesis. There may be one or more reactants missing from the left-hand side, but there are no products missing from the right-hand side. There may also be catalysts, small inorganic reagents, and other important reaction conditions missing from the arrow. • Is the student's transformation possible? If not, check the box under the drawing area. . If the student's transformation is possible, then complete the reaction by adding any missing reactants to the left-hand side, and adding required catalysts, inorganic reagents, or other important reaction conditions above and below the arrow. • You do not need to balance the reaction, but be sure every important organic reactant or product is shown. + T X O O лет-ле HO OH HO OH This transformation can't be done in one step.arrow_forwardDetermine the structures of the missing organic molecules in the following reaction: X+H₂O H* H+ Y OH OH Note: Molecules that share the same letter have the exact same structure. In the drawing area below, draw the skeletal ("line") structures of the missing organic molecules X and Y. You may draw the structures in any arrangement that you like, so long as they aren't touching. Click and drag to start drawing a structure. X Sarrow_forward
- Predict the major products of this organic reaction. If there aren't any products, because nothing will happen, check the box under the drawing area instead. No reaction. HO. O :☐ + G Na O.H Click and drag to start drawing a structure. XS xs H₂Oarrow_forwardWhat are the angles a and b in the actual molecule of which this is a Lewis structure? H H C H- a -H b H Note for advanced students: give the ideal angles, and don't worry about small differences from the ideal groups may have slightly different sizes. a = b = 0 °arrow_forwardWhat are the angles a and b in the actual molecule of which this is a Lewis structure? :0: HCOH a Note for advanced students: give the ideal angles, and don't worry about small differences from the ideal that might be caused by the fact that different electron groups may have slightly different sizes. a = 0 b=0° Sarrow_forward
- Determine the structures of the missing organic molecules in the following reaction: + H₂O +H OH O OH +H OH X Note: Molecules that share the same letter have the exact same structure. In the drawing area below, draw the skeletal ("line") structure of the missing organic molecule X. Click and drag to start drawing a structure.arrow_forwardIdentify the missing organic reactant in the following reaction: x + x O OH H* + ☑- X H+ O O Х Note: This chemical equation only focuses on the important organic molecules in the reaction. Additional inorganic or small-molecule reactants or products (like H₂O) are not shown. In the drawing area below, draw the skeletal ("line") structure of the missing organic reactant X. Click and drag to start drawing a structure. Carrow_forwardCH3O OH OH O hemiacetal O acetal O neither O 0 O hemiacetal acetal neither OH hemiacetal O acetal O neither CH2 O-CH2-CH3 CH3-C-OH O hemiacetal O acetal CH3-CH2-CH2-0-c-O-CH2-CH2-CH3 O neither HO-CH2 ? 000 Ar Barrow_forward
- What would be the best choices for the missing reagents 1 and 3 in this synthesis? 1. PPh3 2 2. n-BuLi 3 Draw the missing reagents in the drawing area below. You can draw them in any arrangement you like. • Do not draw the missing reagent 2. If you draw 1 correctly, we'll know what it is. • Note: if one of your reagents needs to contain a halogen, use bromine. Explanation Check Click and drag to start drawing a structure.arrow_forwardPredict the products of this organic reaction: NaBH3CN + NH2 ? H+ Click and drag to start drawing a structure. ×arrow_forwardPredict the organic products that form in the reaction below: + OH +H H+ ➤ ☑ X - Y Note: You may assume you have an excess of either reactant if the reaction requires more than one of those molecules to form the products. In the drawing area below, draw the skeletal ("line") structures of the missing organic products X and Y. You may draw the structures in any arrangement that you like, so long as they aren't touching. Click and drag to start drawing a structure. Garrow_forward
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