Washing soda, a compound used to prepare hard water for washing laundry, is a hydrate, which means that a certain number of water molecules are included in the solid structure. Its formula can be written as Na2CO3 # xH2O, where x is the number of moles of H2O per mole of Na2CO3. When a 2.558-g sample of washing soda is heated at 125 C, all the water of hydration is lost, leaving 0.948 g of Na2CO3. What is the value of x?

Video transcript

Welcome back everyone to another video washing soda. A compound used to prepare hard water is a hydrate, which means that a certain number of water molecules are included in a solid structure. Its formula can be written as sodium carbonate X hydrate where X is the number of moles of water per mole of sodium carbonate. A 6.51 g sample of washing soda is heated at 125 °C and all the water of hydration is lost leaving 1.48 g of sodium carbonate. What is the value of X? We are given four answer choices. A 10 B 20 C 15 and D 18. So first of all, what we're going to do is just write the balance equation. We have sodium carbonate egg hydrate solid. And essentially when we heat it at 125 °C, we are releasing solid sodium carbonate and water vapor, right? Because the temperature is above 100 degrees. Now, from here, we can think about our next step, right? We can easily find the mass of each product. First of all, we are given that the mass of sodium carbonate is equal to 1.48 g. Meaning the mass of water, according to the law of energy conservation will be the difference between the mass of the sample and the mass of sodium carbonate. So that'll be 6.51 g minus 1.48 g, which essentially gives us 5.03 g. Our next step is to calculate the number of moles of each. So starting with sodium carbonate, we take its mass and divide by the molar mass of the substance. The molar mass of sodium carbonate would be 106.0 g per mole. This gives us zero point 013, 96 moles. And now for the number of moles of water, we take its mass 5.03 grams and we divide by the molar mass of water which is 18.015 g per mole. We end up with 0.2781 moles. Therefore, what we want to do to find a is simply divide the number of moles of water by the number of moles of sodium carbonate. So we get the number of moles of water per one mole of sodium carbonate. We take 0.2781 moles and we divide that by 0.01396 moles. And from here, we can clearly see that the valley of X would be 20 which corresponds to the answer choice B and the multiple choice that would be it for today. And thank you for watching.