Tutor profile: Sachin P.
Traduce la siguiente frase al inglés: Ayer mi gato se escapó de mi casa y corrió en la calle mientras llovía y tuve que perseguirlo; lo cogí antes de que un coche lo atropellara, pero ahora tengo un resfriado por la lluvia.
Yesterday my cat escaped from my house and ran into the street while it was raining and I had to chase him; I caught him before a car ran him over, but now I have a cold because of the rain.
For the combustion of methane to form carbon dioxide and water, CH4 + O2 --> CO2 + H2O, (a) balance the chemical equation (b) identify atoms that are oxidized/reduced in this reaction.
(a) The only sources of carbon are CH4 (on the reactants side) and CO2 (on the products side). Therefore, we need a ratio of 1:1 of these two molecules in order to balance the number of carbon atoms in equation. The only sources of hydrogen are CH4 (on the reactants side) and H2O (on the products side), so in order to balance the equation, we need two molecules of H2O for every one of CH4 in order to balance the hydrogens in the equation. On the products side, now, we have one molecule of CO2 and two molecules of H2O, for a total of four oxygen atoms. This means that we need four oxygen atoms on the reactants side, so there must be two O2 molecules to balance the reaction. Therefore, the balanced equation is CH4 + 2 O2 --> CO2 + 2 H2O (b) We must first assign oxidation numbers to each atom in this reaction. On the reactants side, each H is +1 so the C must be -4, and each O is 0. On the products side, each O is -2 and each H is +1, making the C +4. Comparing these numbers, we see the oxidation number of carbon increase while the oxidation number of all oxygen atoms decreases. Therefore, carbon is oxidized and oxygen is reduced.
Solve the following system of equations: $$x - 3y + 4z = 0$$ $$2x - y + 2z = 3$$ $$y - x - z = 0$$
To solve this, I would first add the first and third equations together to get the result $$3z - 2y = 0$$, or $$y = 3z/2$$. Inserting this expression in place of $$y$$ in the second equation, we get $$2x - 3z/2 + 2z = 3$$, or $$2x + z/2 = 3$$, which simplifies to $$x = (6 - z)/4$$. Inserting this expression in place of $$x$$ the previous expression for $$y$$ into the first equation, we see $$(6-z)/4 - 3*(3z/2) + 4z = 0$$, or $$6 - z - 18z + 16z = 0$$, so $$z = 2$$. We can plug this into the above expressions for $$x$$ and $$y$$ in terms of $$z$$ to get the final result: $$x = 1, y = 3, z = 2$$
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