An ice cube that is 25.00 g (temp -20 C) is placed into 225.00 g of H2O that is

Question

An ice cube that is 25.00 g (temp -20 C) is placed into 225.00 g of H2O that is 22 degrees C. What will the temperature be when the ice cube has just melted. Use 4.184 J/K*g for the specific heat capacity of ice and water. If the water is then heated to 80 degrees C by burning methane (delta H= =890.31 kJ/mol) how many grams of methane would you have to use?

Explanation / Answer

In order to solve this question, you must first find the balanced equation of the reaction. A balanced equation is an equation of a reaction in which mass, energy, and number of atoms remain the same. In this case, X moles of C reacts with X moles of H2 (since it is a diatomic element) to make X moles of CH4 If we have the same amount of atoms on the same side of the equation, the balanced equation would end up being 1 C + 2 H2 --> 1 CH4 This equation will serve as the basis of comparison for your actual problem. The balanced equation measure the MOLES of each substance, not GRAMS. In order to solve, you must convert each amount into moles using the equation Moles = grams of substance / gram formula mass So if we use this equation, you will have. X moles = 3.0 g / 1 g = 3 Moles of Hydrogen X moles = 20.0 g / 12 g = 1.66666666....7 moles = 1.7 moles of Carbon From there, you will used the balanced equation to find out the amount of methane that can be produced. One of the amounts of Hydrogen or Carbon will become a limiting factor, which limits the amount of total product that can be reduced. To take account for this, you have to put both of the amounts into the mole ratios in the equation. The mole ratios in the balanced equation suggest that 1 moles C + 2 moles H2 ---> 1 moles CH4 So if we have 3 moles of Hydrogen, you will need to multiply that number by 1) The ratio of carbon to hydrogen to the amount of carbon it takes to react completely with 3 moles of hydrogen. 2) The ratio of hydrogen to methan, in which 3 moles of Hydrogen will create X amount of methane. So when we calculate it, it should look like this. 1) 3 moles of H2 x 2 moles of C /1 mole of H2 = 6 moles of carbon needed to react 2) 3 moles of H2 x 1 mole of CH4 / 1 moles of H2 = 3 moles of CH4 Repeat this process with Carbon. You will have to use the following ratios 1) The ratio of carbon to hydrogen to see how much hydrogen is needed to react 2) The ratio of carbon to methane to see how much methane can be produced. This will look like this. 1) 1.7 moles of C x 1 mole of H2 / 2 moles of C = 0.85 moles of H2 2) 1.7 moles of C x 1 moles of CH4 / 2 moles of C = 0.85 moles of H2 Comparing the two results of step 1, you see that carbon becomes the limiting factor, as the total amount of carbon (1.7 moles) fully reacts with only 0.85 moles of H2, while the amount of hydrogen needs a total of 6 moles of carbon to fully react. This leaves you with an extra 2.15 moles of Hydrogen. Upon determining this, you will use the amount of methane produced in step 2 with Carbon, which is 0.85 grams of CH4. The last step is to convert this amount to grams using the same equation used to determine the number of moles. 0.85 moles = x grams / 16 g = 13.6 g of methane.

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