Choose one and write out Ka expression for one of the conditions below and calculate the pH based on lab results below. Be sure to show every step of your work. (Using Table 11. 10 and PDF - Nursing Quick Reference for Health) :
i) Respiratory Acidosis
(HCO3- Within Normal Limit (WNL), pCO2 Increase, pH decrease)
(1) [H2CO3] = 55.8 mmole/L
(2) [HCO3- ] = 24 mmole/L (WNL)
ii) Metabolic Acidosis
(HCO3- decrease, pCO2 WNL, pH decrease)
(1) [H2CO3] = 2.4 mmole/L (WNL)
(2) [HCO3-] = 8 mmole/L
iii) Respiratory Alkalosis – Hyperventilation
(HCO3- WNL, pCO2 decrease, pH increase)
(1) [H2CO3] = 1.4 mmole/L
(2) [HCO3] = 24 mmole/L (WNL)
iv) Metabolic Alkalosis.
(HCO3- increase, pCO2 WNL, pH increase)
(1) [H2CO3] = 2.4 mmole/L (WNL)
(2) [HCO3] = 35 mmole/L
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i) Respiratory Acidosis (HCO3- Within Normal Limit (WNL), pCO2 Increase, pH decrease)
Step 1: Write out the equation for the dissociation of carbonic acid (H2CO3):
H2CO3 ⇌ H+ + HCO3-
Step 2: Write out the expression for the acid dissociation constant (Ka) for this reaction:
Ka = [H+][HCO3-] / [H2CO3]
Step 3: Substitute the given values into the Ka expression:
[H2CO3] = 55.8 mmole/L
[HCO3-] = 24 mmole/L
Ka = [H+][24] / 55.8
Step 4: Calculate the concentration of H+:
[H+] = Ka * 55.8 / 24
Step 4: Calculate the pH using the concentration of H+:
pH = -log[H+]
ii) Metabolic Acidosis (HCO3- decrease, pCO2 WNL, pH decrease)
Step 1: Write out the equation for the dissociation of carbonic acid (H2CO3):
H2CO3 ⇌ H+ + HCO3-
Step 2: Write out the expression for the acid dissociation constant (Ka) for this reaction:
Ka = [H+][HCO3-] / [H2CO3]
Step 3: Substitute the given values into the Ka expression:
[H2CO3] = 2.4 mmole/L
[HCO3-] = 8 mmole/L
Ka = [H+][8] / 2.4
Step 4: Calculate the concentration of H+:
[H+] = Ka * 2.4 / 8
Step 5: Calculate the pH using the concentration of H+:
pH = -log[H+]
iii) Respiratory Alkalosis - Hyperventilation (HCO3- WNL, pCO2 decrease, pH increase)
Step 1: Write out the equation for the dissociation of carbonic acid (H2CO3):
H2CO3 ⇌ H+ + HCO3-
Step 2: Write out the expression for the acid dissociation constant (Ka) for this reaction:
Ka = [H+][HCO3-] / [H2CO3]
Step 3: Substitute the given values into the Ka expression:
[H2CO3] = 1.4 mmole/L
[HCO3-] = 24 mmole/L
Ka = [H+][24] / 1.4
Step 4: Calculate the concentration of H+:
[H+] = Ka * 1.4 / 24
Step 5: Calculate the pH using the concentration of H+:
pH = -log[H+]
iv) Metabolic Alkalosis (HCO3- increase, pCO2 WNL, pH increase)
Step 1: Write out the equation for the dissociation of carbonic acid (H2CO3):
H2CO3 ⇌ H+ + HCO3-
Step 2: Write out the expression for the acid dissociation constant (Ka) for this reaction:
Ka = [H+][HCO3-] / [H2CO3]
Step 3: Substitute the given values into the Ka expression:
[H2CO3] = 2.4 mmole/L
[HCO3-] = 35 mmole/L
Ka = [H+][35] / 2.4
Step 4: Calculate the concentration of H+:
[H+] = Ka * 2.4 / 35
Step 5: Calculate the pH using the concentration of H+:
pH = -log[H+]
To calculate the pH based on the given lab results, we need to calculate the concentration of H+ ions using the Ka expression for each condition. Let's go through each condition and calculate the pH step by step:
i) Respiratory Acidosis:
Ka expression for H2CO3 (carbonic acid):
Ka = [H+][HCO3-] / [H2CO3]
Given:
[H2CO3] = 55.8 mmole/L
[HCO3-] = 24 mmole/L
Since we need to find the pH, we are interested in the concentration of [H+]. Assuming H2CO3 is completely dissociated into H+ and HCO3-, we can rewrite the Ka expression as:
Ka = [H+][HCO3-] / 55.8 (since [H2CO3] = [HCO3-])
Since we have two unknowns [H+] and [HCO3-] and only one equation, we need to know the concentration of [HCO3-] or pCO2 to solve for [H+]. Please provide additional information regarding pCO2 or HCO3- if available.
ii) Metabolic Acidosis:
Ka expression for H2CO3 (carbonic acid):
Ka = [H+][HCO3-] / [H2CO3]
Given:
[H2CO3] = 2.4 mmole/L
[HCO3-] = 8 mmole/L
Using the given values, we can substitute them into the Ka expression:
Ka = [H+][8] / 2.4
We have one equation and one unknown ([H+]), so we can solve for [H+] using basic algebra:
[H+] = (Ka * [H2CO3]) / [HCO3-]
= (Ka * 2.4) / 8
Now, we can calculate the pH using the equation:
pH = -log[H+]
Substitute the value of [H+] calculated above into the equation to find the pH.
iii) Respiratory Alkalosis – Hyperventilation:
Ka expression for H2CO3 (carbonic acid):
Ka = [H+][HCO3-] / [H2CO3]
Given:
[H2CO3] = 1.4 mmole/L
[HCO3] = 24 mmole/L
Using the given values, we can substitute them into the Ka expression:
Ka = [H+][24] / 1.4
We have one equation and one unknown ([H+]), so we can solve for [H+] using basic algebra:
[H+] = (Ka * [H2CO3]) / [HCO3]
= (Ka * 1.4) / 24
Now, we can calculate the pH using the equation:
pH = -log[H+]
Substitute the value of [H+] calculated above into the equation to find the pH.
iv) Metabolic Alkalosis:
Ka expression for H2CO3 (carbonic acid):
Ka = [H+][HCO3-] / [H2CO3]
Given:
[H2CO3] = 2.4 mmole/L
[HCO3] = 35 mmole/L
Using the given values, we can substitute them into the Ka expression:
Ka = [H+][35] / 2.4
We have one equation and one unknown ([H+]), so we can solve for [H+] using basic algebra:
[H+] = (Ka * [H2CO3]) / [HCO3]
= (Ka * 2.4) / 35
Now, we can calculate the pH using the equation:
pH = -log[H+]
Substitute the value of [H+] calculated above into the equation to find the pH.
Please note that the values of Ka for H2CO3 are not provided. To accurately calculate the pH, you will need the value of Ka or additional information.