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kotegsom [21]
3 years ago
9

Consider 1 mol an ideal gas at 28∘ C and 1.06 atm pressure. To get some idea how close these molecules are to each other, on the

average, imagine them to be uniformly spaced, with each molecule at the center of a small cube.
A) What is the length of an edge of each cube if adjacent cubes touch but do not overlap?

B) How does this distance compare with the diameter of a typical molecule? The diameter of a typical molecule is about 10-10 m. (in l/dmolecule)

C) How does their separation compare with the spacing of atoms in solids, which typically are about 0.3 nm apart? (in l/lsolid)
Physics
1 answer:
Makovka662 [10]3 years ago
6 0

Answer:

A) Length of an edge = 3.38 × 10^(-9) m

B) 34 times the diameter of a molecule.

C) 11 times the atomic spacing in solids.

Explanation:

A) We will use Avogadro's hypothesis to solve this. It states that 1 mole of gas occupies 22.4 L at STP.

We want to find the volume occupied by 1 mole of gas at 1.06 atm pressure and temperature of 28 °C (= 301 K).

Thus, by the ideal gas equation, we have;

V_mole = (1 × 22.4/273) × (301/1.06) = 23.3 L = 0.0233 m³

Now, since from avogadros number, 1 mole of gas contains 6.02 x 10^(23) molecules, then volume occupied by a molecule is given by;

V_molecule = 0.0233/(6.02 × 10^(23)) m³ = 3.87 x 10^(-26) m³

Thus, length of an edge of the cube = ∛(3.87 × 10^(-26)) = 3.38 × 10^(-9) m

B) We are told that The diameter of a typical molecule is about 10^(-10) m.

Thus, the distance is about;

(3.38 × 10^(-9))/(10^(-10)) ≈ 34 times the diameter of a molecule.

C) We are told that the spacing of atoms is typically are about 0.3 nm apart

Thus;

The separation will be about;

(3.38 × 10^(-9))/(0.3 × 10^(-9)) ≈ 11 times the atomic spacing in solids.

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sergeinik [125]

Answer:

a) 80 V

b) The magnitude of the electric field is 100 N/C and the direction of the electric field is from point B to point A where the electric field is toward the negative charge

Explanation:

<u>Given :</u>

We are given an object with charge q = -6.00 x I0^-9 C starts moving from the rest at point A, which means its kinetic energy at point A is zero ( K_{A}= 0) to the point B at distance l = 0.500m where its kinetic energy is (  K_{B}= 5.00 x 10^-7J) . Also, the electric potential of q at point A is VA = + 30.0 v.

<u>Required :</u>

<em>(a) We are asked to find the electric potential VB </em>

<em>(b) We want to determine the magnitude and the direction of the electric field E. </em>

<u> Solution </u>

(a) We are given the values for VA,K_{B} and q so we want to find a relationship between these three parameters and VB to get the value of VB.

As we have two states, at points A and B , where the charge moved from A to B due to the applied electric field. The mechanical energy of the object is conservative during this travel, and we can apply eq(1) in this situation:

                                   K_{A} +U_{A} =K_{B} +U_{B} .........................................(1)                                          

Where K_{A}= 0 and the potential energy U of the charge is given by U = q V

where V is the electric potential.  So, equation (1) will be in the form :

                                  0+qVA=K_{B} +qVB                      (Divide by q)

                                         VA=K_{B} /q + VB                  (solve for VB)

                                         VB=VA- K_{B}/q .......................................(2)

We get the relation between VB, VA and K_{B}, now we can plug our values for VA, K_{B} and q into equation (2) to get VB

                                         VB=VA- K_{B}/q

                                              =30V-(5.00 x 10^-7J)/(-6.00 x I0^-9)

                                              =80 V

(b) After we calculated VB we can use equation a to get the electric field E that applied to the charge q, where the potential difference between the two points equals the integration of the electric field multiplied by the distance l between the two points

                                   VA-VB =\int\limits^1_0 {E} \, dl...................................(a)

                                               =E\int\limits^1_0 {} \, dl

                                   VA-VB=El                      (solve for E)

                                            E= VA-VB/l..................................(3)

Now let us plug our values for VA, Vs and l into equation (3) to get the electric field E

                                            E= VA-VB/l

                                              =-100 N/C

The magnitude of the electric field is 100 N/C and the direction of the electric field is from point B to point A where the electric field is toward the negative charge

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