Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Problem 59

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 \(\mathrm{Na}_{2} \mathrm{CO}_{3} \cdot x \mathrm{H}_{2} \mathrm{O},\) where \(x\) is the number of moles of \(\mathrm{H}_{2} \mathrm{O}\) per mole of \(\mathrm{Na}_{2} \mathrm{CO}_{3} .\) When a 2.558 -g sample of washing soda is heated at \(125^{\circ} \mathrm{C}\) , all the water of hydration is lost, leaving 0.948 \(\mathrm{g}\) of \(\mathrm{Na}_{2} \mathrm{CO}_{3} .\) What is the value of \(x ?\)

Short Answer

Expert verified
The value of x in the formula \(\mathrm{Na}_2\mathrm{CO}_3 \cdot x\mathrm{H}_2\mathrm{O}\) for washing soda hydrate is 10, making the formula \(\mathrm{Na}_2\mathrm{CO}_3\cdot10\mathrm{H}_2\mathrm{O}\).

Step by step solution

01

Calculate the moles of \(\mathrm{Na}_2\mathrm{CO}_3\) after heating

First, we need to find the moles of \(\mathrm{Na}_{2}\mathrm{CO}_{3}\) using the given mass after heating (0.948 g) and the molar mass of \(\mathrm{Na}_{2}\mathrm{CO}_{3}\). The molar mass of \(\mathrm{Na}_2\mathrm{CO}_3\) is \(2\times23.0 (\mathrm{Na}) + 12.0 (\mathrm{C}) + 3\times16.0 (\mathrm{O}) = 106.0 \,\mathrm{g/mol}\). Now, we can calculate the moles of \(\mathrm{Na}_{2}\mathrm{CO}_{3}\) as: \[\frac{0.948\;\text{g}}{106.0\;\text{g/mol}} = 0.00894\;\text{mol}\]
02

Calculate the mass of the water of hydration released

To find the mass of the water of hydration, we subtract the mass of \(\mathrm{Na}_2\mathrm{CO}_3\) after heating from the mass of the hydrate before heating: \[2.558 \; \text{g} - 0.948 \;\text{g} = 1.610 \;\text{g}\]
03

Calculate the moles of water of hydration released

Now, we need to find the moles of the water of hydration released. To do this, we will use the mass of water released (1.610 g) and the molar mass of water, which is \(2\times1.0 (\mathrm{H}) + 16.0 (\mathrm{O}) = 18.0 \,\mathrm{g/mol}\). Now, we can calculate the moles of \(\mathrm{H}_2\mathrm{O}\) as: \[\frac{1.610\;\text{g}}{18.0\;\text{g/mol}} = 0.0894\;\text{mol}\]
04

Determine the value of \(x\) by calculating the ratio of moles

We now have the moles of \(\mathrm{Na}_2\mathrm{CO}_3\) (0.00894 mol) and the moles of \(\mathrm{H}_2\mathrm{O}\) (0.0894 mol) present in the washing soda. To find the value of x, we need to find the ratio of the moles of \(\mathrm{H}_2\mathrm{O}\) to moles of \(\mathrm{Na}_2\mathrm{CO}_3\): \[x = \frac{\text{moles of }\mathrm{H}_2\mathrm{O}}{\text{moles of }\mathrm{Na}_2\mathrm{CO}_3} = \frac{0.0894\;\text{mol}}{0.00894\;\text{mol}} = 10\] So, the value of x is 10, and the formula of the washing soda hydrate is \(\mathrm{Na}_2\mathrm{CO}_3\cdot10\mathrm{H}_2\mathrm{O}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Give the empirical formula of each of the following compounds if a sample contains (a) 0.0130 mol \(\mathrm{C}, 0.0390 \mathrm{mol}\) \(\mathrm{H},\) and \(0.0065 \mathrm{mol} \mathrm{O} ;\) (b) \(11.66 \mathrm{g}\) iron and 5.01 \(\mathrm{g}\) oxygen; (c) \(40.0 \% \mathrm{C}, 6.7 \% \mathrm{H},\) and 53.3\(\%\) o by mass.

Vanillin, the dominant flavoring in vanilla, contains \(\mathrm{C}, \mathrm{H}\) , and \(\mathrm{O} .\) When 1.05 \(\mathrm{g}\) of this substance is completely combusted, 2.43 \(\mathrm{g}\) of \(\mathrm{CO}_{2}\) and 0.50 \(\mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O}\) are produced. What is the empirical formula of vanillin?

The fizz produced when an Alka-Seltzer tablet is dissolved in water is due to the reaction between sodium bicarbonate \(\left(\mathrm{NaHCO}_{3}\right)\) and citric acid \(\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right) :\) $$ \begin{aligned} 3 \mathrm{NaHCO}_{3}(a q)+\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q) & \longrightarrow \\ & 3 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q) \end{aligned} $$ In a certain experiment 1.00 g of sodium bicarbonate and 1.00 g of citric acid are allowed to react. (a) Which is the limiting reactant? (b) How many grams of carbon dioxide form? (c) How many grams of the excess reactant remain after the limiting reactant is completely consumed?

When hydrocarbons are burned in a limited amount of air, both CO and \(\mathrm{CO}_{2}\) form. When 0.450 g of a particular hydrocarbon was burned in air, 0.467 \(\mathrm{g}\) of \(\mathrm{CO}, 0.733 \mathrm{g}\) of \(\mathrm{CO}_{2},\) and 0.450 \(\mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O}\) were formed. (a) What is the empirical formula of the compound? (b) How many grams of O \(_{2}\) were used in the reaction? (c) How many grams would have been required for complete combustion?

Without doing any detailed calculations (but using a periodic table to give atomic weights, rank the following samples in order of increasing numbers of atoms: 42 gof NaHCO \(_{3}, 1.5 \mathrm{mol} \mathrm{CO}_{2}, 6.0 \times 10^{24} \mathrm{Ne}\) atoms.
See all solutions

Recommended explanations on Chemistry Textbooks

Making Measurements

Read Explanation

The Earths Atmosphere

Read Explanation

Organic Chemistry

Read Explanation

Kinetics

Read Explanation

Chemical Reactions

Read Explanation

Chemistry Branches

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free