Math / Data & Statistics

QuestionYou have a trauma patient in the ER on 3 L nasal cannula. Their PaO 2 is 95 , hemoglobin is 4 , and SaO 2 is $95 \%$ . What is their CaO 2 ? 5.4 25.8 10.8 20.6

Studdy Solution

STEP 1

What is this asking? We need to calculate the total arterial oxygen content ( $CaO_2$ ) in a patient's blood, given their partial pressure of oxygen, hemoglobin level, and oxygen saturation. Watch out! Don't forget to convert the hemoglobin level from g/dL to g/100mL, and remember to account for dissolved oxygen, even though it's a small part of the total oxygen content!

STEP 2

1. Calculate the oxygen bound to hemoglobin.
2. Calculate the dissolved oxygen.
3. Calculate the total arterial oxygen content.

STEP 3

Alright, let's break down this $CaO_2$ calculation!
First, we'll tackle the oxygen bound to hemoglobin.
The formula is: $(1.34 \cdot Hb \cdot SaO_2)$ , where $Hb$ is the hemoglobin level and $SaO_2$ is the oxygen saturation.
This formula tells us how much oxygen each red blood cell can carry!

STEP 4

We're given $Hb = 4$ g/dL, and we need it in g/100mL.
Since 1 dL = 100 mL, our hemoglobin level is already in the correct units!
Our $SaO_2$ is 95%, which we'll use as 0.95 in the formula.

STEP 5

Plugging in the values, we get $1.34 \cdot 4 \cdot 0.95 = 5.092$ .
This tells us that 5.092 mL of oxygen is bound to every 100 mL of blood thanks to hemoglobin.

STEP 6

Next up: dissolved oxygen!
The formula is $(PaO_2 \cdot 0.003)$ , where $PaO_2$ is the partial pressure of oxygen.
This part of the calculation tells us how much oxygen is floating freely in the blood, not bound to hemoglobin.

STEP 7

We're given $PaO_2 = 95$ mmHg.
Plugging this in, we get $95 \cdot 0.003 = 0.285$ .
So, 0.285 mL of oxygen is dissolved in every 100 mL of blood.

STEP 8

Finally, let's put it all together! $CaO_2$ is simply the sum of the oxygen bound to hemoglobin and the dissolved oxygen.
We add these two values to find the total oxygen content in the arterial blood.

STEP 9

Adding our results from the previous calculations, we have $5.092 + 0.285 = 5.377$ .
Therefore, the $CaO_2$ is 5.377 mL/100mL of blood.

STEP 10

The $CaO_2$ is approximately 5.4 mL/100mL.
So the closest answer is 5.4.

Was this helpful?

QuestionYou have a trauma patient in the ER on 3 L nasal cannula. Their PaO 2 is 95 , hemoglobin is 4 , and SaO 2 is $95 \%$ . What is their CaO 2 ? 5.4 25.8 10.8 20.6

Studdy Solution

STEP 1

STEP 2

1. Calculate the oxygen bound to hemoglobin.
2. Calculate the dissolved oxygen.
3. Calculate the total arterial oxygen content.

STEP 3

Alright, let's break down this $CaO_2$ calculation!
First, we'll tackle the oxygen bound to hemoglobin.
The formula is: $(1.34 \cdot Hb \cdot SaO_2)$ , where $Hb$ is the hemoglobin level and $SaO_2$ is the oxygen saturation.
This formula tells us how much oxygen each red blood cell can carry!

STEP 4

We're given $Hb = 4$ g/dL, and we need it in g/100mL.
Since 1 dL = 100 mL, our hemoglobin level is already in the correct units!
Our $SaO_2$ is 95%, which we'll use as 0.95 in the formula.

STEP 5

Plugging in the values, we get $1.34 \cdot 4 \cdot 0.95 = 5.092$ .
This tells us that 5.092 mL of oxygen is bound to every 100 mL of blood thanks to hemoglobin.

STEP 6

Next up: dissolved oxygen!
The formula is $(PaO_2 \cdot 0.003)$ , where $PaO_2$ is the partial pressure of oxygen.
This part of the calculation tells us how much oxygen is floating freely in the blood, not bound to hemoglobin.

STEP 7

We're given $PaO_2 = 95$ mmHg.
Plugging this in, we get $95 \cdot 0.003 = 0.285$ .
So, 0.285 mL of oxygen is dissolved in every 100 mL of blood.

STEP 8

Finally, let's put it all together! $CaO_2$ is simply the sum of the oxygen bound to hemoglobin and the dissolved oxygen.
We add these two values to find the total oxygen content in the arterial blood.

STEP 9

Adding our results from the previous calculations, we have $5.092 + 0.285 = 5.377$ .
Therefore, the $CaO_2$ is 5.377 mL/100mL of blood.

STEP 10

The $CaO_2$ is approximately 5.4 mL/100mL.
So the closest answer is 5.4.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionYou have a trauma patient in the ER on 3 L nasal cannula. Their PaO 2 is 95 , hemoglobin is 4 , and SaO 2 is 95%95 \%95%. What is their CaO 2 ? 5.4 25.8 10.8 20.6

Studdy Solution

STEP 1

STEP 2

1. Calculate the oxygen bound to hemoglobin.2. Calculate the dissolved oxygen.3. Calculate the total arterial oxygen content.

STEP 3

STEP 4

We're given Hb=4Hb = 4Hb=4 g/dL, and we need it in g/100mL.Since 1 dL = 100 mL, our hemoglobin level is already in the correct units!Our SaO2SaO_2SaO2​ is **95%**, which we'll use as **0.95** in the formula.

STEP 5

Plugging in the values, we get 1.34⋅4⋅0.95=5.0921.34 \cdot 4 \cdot 0.95 = 5.0921.34⋅4⋅0.95=5.092.This tells us that **5.092 mL** of oxygen is bound to every **100 mL** of blood thanks to hemoglobin.

STEP 6

Next up: dissolved oxygen!The formula is (PaO2⋅0.003)(PaO_2 \cdot 0.003)(PaO2​⋅0.003), where PaO2PaO_2PaO2​ is the partial pressure of oxygen.This part of the calculation tells us how much oxygen is floating freely in the blood, not bound to hemoglobin.

STEP 7

We're given PaO2=95PaO_2 = 95PaO2​=95 mmHg.Plugging this in, we get 95⋅0.003=0.28595 \cdot 0.003 = 0.28595⋅0.003=0.285.So, **0.285 mL** of oxygen is dissolved in every **100 mL** of blood.

STEP 8

Finally, let's put it all together! CaO2CaO_2CaO2​ is simply the sum of the oxygen bound to hemoglobin and the dissolved oxygen.We add these two values to find the *total* oxygen content in the arterial blood.

STEP 9

Adding our results from the previous calculations, we have 5.092+0.285=5.3775.092 + 0.285 = 5.3775.092+0.285=5.377.Therefore, the CaO2CaO_2CaO2​ is **5.377 mL/100mL** of blood.

STEP 10

The CaO2CaO_2CaO2​ is approximately **5.4 mL/100mL**.So the closest answer is 5.4.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionYou have a trauma patient in the ER on 3 L nasal cannula. Their PaO 2 is 95 , hemoglobin is 4 , and SaO 2 is $95 \%$ . What is their CaO 2 ? 5.4 25.8 10.8 20.6

1. Calculate the oxygen bound to hemoglobin.
2. Calculate the dissolved oxygen.
3. Calculate the total arterial oxygen content.

We're given $Hb = 4$ g/dL, and we need it in g/100mL.
Since 1 dL = 100 mL, our hemoglobin level is already in the correct units!
Our $SaO_2$ is 95%, which we'll use as 0.95 in the formula.

Plugging in the values, we get $1.34 \cdot 4 \cdot 0.95 = 5.092$ .
This tells us that 5.092 mL of oxygen is bound to every 100 mL of blood thanks to hemoglobin.

Next up: dissolved oxygen!
The formula is $(PaO_2 \cdot 0.003)$ , where $PaO_2$ is the partial pressure of oxygen.
This part of the calculation tells us how much oxygen is floating freely in the blood, not bound to hemoglobin.

We're given $PaO_2 = 95$ mmHg.
Plugging this in, we get $95 \cdot 0.003 = 0.285$ .
So, 0.285 mL of oxygen is dissolved in every 100 mL of blood.

Finally, let's put it all together! $CaO_2$ is simply the sum of the oxygen bound to hemoglobin and the dissolved oxygen.
We add these two values to find the total oxygen content in the arterial blood.

Adding our results from the previous calculations, we have $5.092 + 0.285 = 5.377$ .
Therefore, the $CaO_2$ is 5.377 mL/100mL of blood.

The $CaO_2$ is approximately 5.4 mL/100mL.
So the closest answer is 5.4.