Sodium (Na) metal undergoes a chemical reaction with chlorine (Cl) gas to yield sodium Cl, or common table salt. If 1.00 g of sodium reacts with 1.54 g of chlorine, 2.54 g of sodium chloride is formed and 17.9 kJ of heat is released. How much sodium and how much chlorine is grams would have to react to release 171 kcal of heat?
I don't understand what you mean by dividing it into the required ratio. I understand where you got the ratio from, but do you mean 24.26/1.00 = for sodium and 24.26/1.54 = for chlorine?
171kcal * 2.54g NaCl/17.9kcal = 24.26g NaCl
Now divide that up into the required 1:1.54 ratio to get the amount of each
To solve this problem, let's start by calculating the amount of heat released per gram of sodium chloride formed:
Heat released = 17.9 kJ
Mass of sodium chloride formed = 2.54 g
Heat released per gram of sodium chloride = 17.9 kJ / 2.54 g
Heat released per gram of sodium chloride = 7.047 kJ/g
Next, we need to convert the given heat to kilojoules (kJ) since the conversion factor is kcal to kJ:
Given heat = 171 kcal
To convert kcal to kJ, we know that 1 kcal is equal to 4.18 kJ. Therefore:
Given heat in kJ = 171 kcal × 4.18 kJ/kcal
Given heat in kJ = 714.78 kJ
Now, let's calculate the amount of sodium chloride formed in grams that would release 171 kcal of heat:
Mass of sodium chloride formed = 714.78 kJ / (heat released per gram of sodium chloride)
Mass of sodium chloride formed = 714.78 kJ / 7.047 kJ/g
Mass of sodium chloride formed = 101.6 g
Finally, we can determine the amount of sodium and chlorine required to form 101.6 g of sodium chloride:
Given mass of sodium chloride formed: 101.6 g
Mass of sodium = (mass of sodium chloride formed / total mass of sodium chloride) × mass of sodium
Mass of sodium = (101.6 g / 2.54 g) × 1.00 g
Mass of sodium = 40.00 g
Mass of chlorine = (mass of sodium chloride formed / total mass of sodium chloride) × mass of chlorine
Mass of chlorine = (101.6 g / 2.54 g) × 1.54 g
Mass of chlorine = 61.00 g
Therefore, 40.0 g of sodium and 61.0 g of chlorine would have to react to release 171 kcal of heat.