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Tutor profile: Abhishek G.

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Abhishek G.
Physics PhD student at a leading research lab in Europe
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Questions

Subject: TOEFL

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Question:

How much did you score in IELTS or TOEFL?

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Abhishek G.
Answer:

Band 9 and 117, respectively.

Subject: Chemistry

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Question:

Why do orbitals hybridize? Does hybridization occur in every molecule?

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Abhishek G.
Answer:

Everything in the chemical world ultimately boils down to energy. Orbitals hybridize because doing so allows the resultant molecule to be lower in energy — and therefore more stable — than if the orbitals did not hybridize. Consider the water molecule, H2O. An unbonded oxygen atom has four orbitals in its valence shell: 2s2, 2p2x, 2p1y, and 2p1z Based on this configuration, you would expect oxygen to form two covalent bonds — one with each hydrogen atom — and that is what happens. However, you would expect the resulting molecule to have an H-O-H bond angle of about 90 degrees, and that is decidedly not the case. Rotational analysis of water’s infrared absorption spectrum shows that the H-O-H bond angle is closer to 104.5 degrees. Why? Because the oxygen atom does not form bonds with its two half-filled 2p orbitals. Instead, as the oxygen atom is bonding with two hydrogen atoms, its orbitals hybridize into four equivalent sp3 orbitals. In doing so, the regions of electron density are able to spread apart, which lowers the electrostatic repulsion between them. The energy needed to rearrange the oxygen atom’s orbitals is more than compensated by the ensuing decrease in potential energy. Does hybridization occur in every molecule? No. Consider a very simple molecule like H2. Each hydrogen atom has only one orbital to start with, so no hybridization can occur. Or consider the molecule HCl. Although the chlorine atom has multiple orbitals, it doesn’t gain much stability by hybridizing them; therefore, it remains unhybridized. Are there any molecules with three or more atoms in which the central atom doesn’t hybridize? Sure. In hydrogen sulfide, H2S, the central sulfur atom apparently does not hybridize! The H-S-H bond angle is only 92.1 degrees — much smaller than the bond angle of water and more in keeping with two unhybridized, orthogonal p orbitals. Why doesn’t the sulfur atom in hydrogen sulfide hybridize? Again, the answer has to do with energy. For one, the 3s and 3p orbitals in sulfur are further apart in energy than are the 2s and 2p orbitals in oxygen, so there’s a greater energy investment needed for hybridization to occur. Furthermore, a sulfur atom is physically larger than an oxygen atom, which means that the hydrogen atoms can bond directly to two of sulfur’s 3p orbitals with less electrostatic repulsion between their bonding pairs. Ergo, the pay-off is not worth the investment, the sulfur atom does not hybridize, and the bond angle in H2S is very nearly a right angle.

Subject: Physics

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Question:

Why does a spacecraft heat up during reentry into atmosphere?

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Abhishek G.
Answer:

The reason why objects without a heat shield or entering the atmosphere uncontrolled incinerate is simply due to the fact air can't get out of their way fast enough. The Space Shuttle strikes the atmosphere at 25 times the speed of sound, and objects coming in from deep space can be moving three or four times faster. As an object encounters the atmosphere, air cannot move out of the way due to the hypersonic velocity, and instead it piles up ahead of the object and compresses into a shock wave. The gases there are compressed rapidly enough to heat up to 20,000 degrees or more, and because of that the radiant heat from the shock wave starts to heat up the incoming object. The heat will either melt or vaporize any material exposed to the shock wave, and since aluminum is used heavily in the construction of spacecraft, the spacecraft tears apart and the pieces melt or vaporize. The shock wave also creates drag upon the object, which slows it down as well and created immense pressures on it as well. If the object has a heat shield, it either melts and burns away, taking the heat with it, or like the Space Shuttle's simply insulates the skin from the heat. This is possible because instead of just diving in like a nuclear bomb or skipping along the atmosphere like a rock off a pond as the Apollo lunar missions did, the Shuttle rides the upper atmosphere like a surfer. That keeps the temperatures low enough for thermal tiles to protect the spacecraft during re-entry. Other spacecraft make a ballistic re-entry, which not only creates hull temperatures of 6,000 degrees and higher, it also treats the crew to severe and sometimes near bone crushing deceleration too. The spacecraft require a very heavy heat shield that cannot be reused, and it burns away to save the spacecraft. The re-entry must be made at a precise angle, or the spacecraft will burn up like a meteorite, or even skip off the atmosphere to careen off into space again. A spacecraft must make a controlled entry no only to avoid breaking apart and burning up, it's also to keep the gee forces from killing the crew.

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