Chapter 13: Problem 9

Soda and lime are added to a glass batch in the form of soda ash \(\left(\mathrm{Na}_{2} \mathrm{CO}_{3}\right)\) and limestone \(\left(\mathrm{CaCO}_{3}\right)\). During heating, these two ingredients decompose to give off carbon dioxide \(\left(\mathrm{CO}_{2}\right)\), the resulting products being soda and lime. Compute the weight of soda ash and limestone that must be added to \(125 \mathrm{lb}_{\mathrm{m}}\) of quartz \(\left(\mathrm{SiO}_{2}\right)\) to yield a glass of composition \(78 \mathrm{wt} \% \mathrm{SiO}_{2}, 17 \mathrm{wt} \% \mathrm{Na}_{2} \mathrm{O}\), and \(5 \mathrm{wt} \% \mathrm{CaO}\)

Short Answer

Expert verified

Answer: To determine the required weights of soda ash (Na₂CO₃) and limestone (CaCO₃), follow these steps: 1. Calculate the total weight of the final glass composition (W_total) and find the weights of Na₂O (W_Na2O) and CaO (W_CaO) in the final glass composition. 2. Find the molar amounts (n_Na2O and n_CaO) of Na₂O and CaO using their respective molar masses. 3. Calculate the required weights of soda ash (W_Na2CO3) and limestone (W_CaCO3) by multiplying the molar amounts of Na₂O and CaO by their respective molar masses of Na₂CO₃ and CaCO₃. By completing these calculations, the required weights of soda ash and limestone can be found for the given glass batch.

Step by step solution

Determine the required weights of Na₂O and CaO in the final glass composition

In order to find the required weights of Na₂O and CaO in the final glass composition, we need to consider the total weight of 125 lbm of quartz and the given percentages of SiO₂, Na₂O, and CaO. We have: - SiO₂: 78 wt% of total glass composition - Na₂O: 17 wt% of total glass composition - CaO: 5 wt% of total glass composition Let's denote the total weight of the final glass batch by \(W_{total}\). We can determine the weight of each component in the glass as follows: 1. \(\frac{78}{100} W_{total} = 125 \Rightarrow W_{total} = \frac{100 \times 125}{78}\) 2. \(W_{Na2O} = \frac{17}{100} W_{total}\) 3. \(W_{CaO} = \frac{5}{100} W_{total}\)

Find the molar amount of Na₂O and CaO

In order to determine the weight of soda ash and limestone, we first need to find the molar quantities of Na₂O and CaO. Using the molar masses of Na₂O (62 g/mol) and CaO (56 g/mol), we can calculate the molar amounts of each component: 1. Moles of Na₂O: \(n_{Na2O} = \frac{W_{Na2O}}{M_{Na2O}}\) 2. Moles of CaO: \(n_{CaO} = \frac{W_{CaO}}{M_{CaO}}\)

Calculate the required weights of soda ash and limestone

Since Na₂O and CaO are produced from the decomposition of soda ash and limestone, respectively, we can calculate the required weights of Na₂CO₃ and CaCO₃ by multiplying the molar amounts of Na₂O and CaO obtained in Step 2 by their respective molar masses. 1. Weight of soda ash: \(W_{Na2CO3} = n_{Na2O} \times M_{Na2CO3}\), where \(M_{Na2CO3}\) is the molar mass of Na₂CO₃ (106 g/mol) 2. Weight of limestone: \(W_{CaCO3} = n_{CaO} \times M_{CaCO3}\), where \(M_{CaCO3}\) is the molar mass of CaCO₃ (100 g/mol). By completing these calculations, we can find the required weights of soda ash and limestone that must be added to the glass batch to obtain the desired composition.

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Short Answer

Step by step solution

Determine the required weights of Na₂O and CaO in the final glass composition

Find the molar amount of Na₂O and CaO

Calculate the required weights of soda ash and limestone

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