Question

chm 1045 module 2 dimensional analysis assignments
part iv. multi - step applications

1. a dialysis machine processes blood at 275 ml/min.

how many liters of blood are processed in 5.0 hours?

1. a metal block has a mass of 325 g and a volume of 41.2 cm³.

calculate the density in kg/m³.

1. a medication is prescribed at 4.5 mg/kg/day.

how many milligrams per day should be administered to a 72 kg patient?

1. liquid nitrogen has a density of 0.808 g/ml.

what is the mass (in kg) of 12.0 l of liquid nitrogen?

1. a cooling system circulates fluid at 1.20 l/min for 45 minutes.

if the fluid density is 1.05 g/ml, determine the total mass of fluid circulated (in kg).

Explanation:

Question 16

Step1: Convert hours to minutes

$5.0\ \text{hours} \times 60\ \frac{\text{min}}{\text{hour}} = 300\ \text{min}$

Step2: Calculate total volume in mL

$275\ \frac{\text{mL}}{\text{min}} \times 300\ \text{min} = 82500\ \text{mL}$

Step3: Convert mL to liters

$82500\ \text{mL} \times \frac{1\ \text{L}}{1000\ \text{mL}} = 82.5\ \text{L}$

Question 17

Step1: Convert mass to kg

$325\ \text{g} \times \frac{1\ \text{kg}}{1000\ \text{g}} = 0.325\ \text{kg}$

Step2: Convert volume to $\text{m}^3$

$41.2\ \text{cm}^3 \times \frac{1\ \text{m}^3}{10^6\ \text{cm}^3} = 4.12 \times 10^{-5}\ \text{m}^3$

Step3: Calculate density

$
ho = \frac{0.325\ \text{kg}}{4.12 \times 10^{-5}\ \text{m}^3} \approx 7888.35\ \frac{\text{kg}}{\text{m}^3}$

Question 18

Step1: Calculate daily dosage

$4.5\ \frac{\text{mg}}{\text{kg}\cdot\text{day}} \times 72\ \text{kg} = 324\ \text{mg/day}$

Question 19

Step1: Convert liters to mL

$12.0\ \text{L} \times 1000\ \frac{\text{mL}}{\text{L}} = 12000\ \text{mL}$

Step2: Calculate mass in g

$0.808\ \frac{\text{g}}{\text{mL}} \times 12000\ \text{mL} = 9696\ \text{g}$

Step3: Convert g to kg

$9696\ \text{g} \times \frac{1\ \text{kg}}{1000\ \text{g}} = 9.696\ \text{kg}$

Question 20

Step1: Calculate total volume of fluid

$1.20\ \frac{\text{L}}{\text{min}} \times 45\ \text{min} = 54\ \text{L}$

Step2: Convert L to mL

$54\ \text{L} \times 1000\ \frac{\text{mL}}{\text{L}} = 54000\ \text{mL}$

Step3: Calculate mass in g

$1.05\ \frac{\text{g}}{\text{mL}} \times 54000\ \text{mL} = 56700\ \text{g}$

Step4: Convert g to kg

$56700\ \text{g} \times \frac{1\ \text{kg}}{1000\ \text{g}} = 56.7\ \text{kg}$

Answer:

1. $82.5\ \text{liters}$
2. $\approx 7888\ \frac{\text{kg}}{\text{m}^3}$
3. $324\ \text{mg per day}$
4. $9.70\ \text{kg}$ (rounded to 3 significant figures)
5. $56.7\ \text{kg}$