A scientist is examining a mixture of nitrogen, hydrogen, and ammonia. The individual pressures that are exerted by nitrogen and hydrogen are [tex]0.26 atm[/tex] and [tex]0.28 atm[/tex], respectively. If the total pressure is [tex]0.90 atm[/tex], what is the partial pressure of ammonia?
Use [tex]P_T=P_1+P_2+P_3+\ldots+P_n[/tex].
A. 0.27 atm
B. 0.36 atm
C. 0.54 atm
D. 0.90 atm
Answer (2)
Use Dalton's Law of Partial Pressures: P T = P N 2 + P H 2 + P N H 3 .
Substitute the given values: 0.90 = 0.26 + 0.28 + P N H 3 .
Solve for the partial pressure of ammonia: P N H 3 = 0.90 − 0.26 − 0.28 .
The partial pressure of ammonia is 0.36 atm .
Explanation
Understanding the Problem We're given a mixture of nitrogen, hydrogen, and ammonia, and we need to find the partial pressure of ammonia. We know the total pressure of the mixture and the partial pressures of nitrogen and hydrogen.
Applying Dalton's Law We can use Dalton's Law of Partial Pressures, which states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each individual gas. The formula is: P T = P N 2 + P H 2 + P N H 3 where:
P T is the total pressure
P N 2 is the partial pressure of nitrogen
P H 2 is the partial pressure of hydrogen
P N H 3 is the partial pressure of ammonia
Identifying Given Values We are given:
P T = 0.90 atm
P N 2 = 0.26 atm
P H 2 = 0.28 atm We need to find P N H 3 .
Solving for the Unknown Substitute the given values into the equation: 0.90 = 0.26 + 0.28 + P N H 3 Now, solve for P N H 3 :
P N H 3 = 0.90 − 0.26 − 0.28 P N H 3 = 0.36 atm
Final Answer The partial pressure of ammonia is 0.36 atm.
Examples
Understanding partial pressures is crucial in various real-world applications. For instance, in scuba diving, knowing the partial pressures of oxygen and nitrogen helps divers calculate safe depths and avoid nitrogen narcosis. Similarly, in anesthesia, controlling the partial pressures of different gases ensures the patient remains unconscious and pain-free. In industrial chemistry, understanding partial pressures helps optimize reaction conditions for maximum yield.
The partial pressure of ammonia in the mixture is calculated using Dalton's Law of Partial Pressures, concluding that P N H 3 = 0.36 atm . Therefore, the correct answer is B. 0.36 atm.
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