Two chemicals A and B are combined to form a chemical C. The rate, or velocity, of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C. Initially, there are 40 grams of A and 50 grams of B, and for each gram of B, 2 grams of A is used. It is observed that 10 grams of C is formed in 10 minutes. How much (in grams) is formed in 20 minutes? (Round your answer to one decimal place.) grams What is the limiting amount (in grams) of C after a long time? grams How much (in grams) of chemicals A and B remains after a long time? grams B grams
Two chemicals A and B are combined to form a chemical C. The rate, or velocity, of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C. Initially, there are 40 grams of A and 50 grams of B, and for each gram of B, 2 grams of A is used. It is observed that 10 grams of C is formed in 10 minutes. How much (in grams) is formed in 20 minutes? (Round your answer to one decimal place.) grams What is the limiting amount (in grams) of C after a long time? grams How much (in grams) of chemicals A and B remains after a long time? grams B grams
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:**Title: Chemical Reaction Rate and Limiting Reactant Analysis**
**Introduction:**
In this exploration, we consider a chemical reaction where two reactants, A and B, combine to form a product, C. We will analyze the rate of reaction, the limiting reactant, and the remaining quantities of A and B over time.
**Chemical Reaction Details:**
Two chemicals, A and B, are combined to produce chemical C. The rate or velocity of this reaction is directly proportional to the product of the instantaneous amounts of A and B that have not yet been converted to C.
**Initial Conditions:**
- Initial amount of A: **40 grams**
- Initial amount of B: **50 grams**
- Conversion ratio: For each gram of B, **2 grams** of A are used.
**Observations:**
- **10 grams** of C are formed in **10 minutes**.
**Questions to Consider:**
1. **Amount of C Formed in 20 Minutes:**
- Calculate how many grams of C are formed in 20 minutes. (Round your answer to one decimal place.)
- **Answer:** __ grams
2. **Limiting Amount of C After a Long Time:**
- Determine the limiting amount (in grams) of C after a long time.
- **Answer:** __ grams
3. **Remaining Quantities of A and B:**
- How much (in grams) of each chemical remains after a long time?
- A: **__ grams**
- B: **__ grams**
This exercise provides an opportunity to practice calculations related to reaction rates, limiting reactants, and the long-term behaviors of chemical reactions.
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