Using the following unit conversions

5. Using the following unit conversions: 1.00 fluid ounce = 29.573 ml, 1.00 L = 1000 cm
   , density of water = 1.00 gm/cm
   , the number of fluid ounces in a kg of water is

The Correct Answer and Explanation is:

To calculate the number of fluid ounces in a kilogram (kg) of water, we will use the unit conversions and the properties of water provided:

Given:

• 1.00 fluid ounce = 29.573 mL
• 1.00 liter (L) = 1000 cm³
• Density of water = 1.00 gm/cm³

Step-by-step Solution:

1. Start with the mass of water:
   A kilogram (kg) of water is 1000 grams (since 1 kg = 1000 grams).
2. Convert grams of water to volume in cm³:
   The density of water is 1.00 gm/cm³, meaning that the mass in grams is equal to the volume in cm³. So, 1000 grams of water will occupy 1000 cm³ of space.
3. Convert cm³ to liters:
   Since 1 liter = 1000 cm³, we can directly convert the 1000 cm³ of water into 1 liter of water.
4. Convert liters to fluid ounces:
   Now, we know that:
   • 1 liter = 1000 mL
   • And 1 fluid ounce = 29.573 mL.
   Therefore, to convert 1000 mL into fluid ounces: Number of fluid ounces=1000 mL29.573 mL/oz=33.814 fluid ounces.\text{Number of fluid ounces} = \frac{1000 \, \text{mL}}{29.573 \, \text{mL/oz}} = 33.814 \, \text{fluid ounces}.Number of fluid ounces=29.573mL/oz1000mL​=33.814fluid ounces.

Conclusion:

The number of fluid ounces in 1 kg of water is approximately 33.814 fluid ounces.

This calculation uses the relationship between mass, volume, and density, along with unit conversion factors. Since water has a density of 1 gm/cm³, the volume in cm³ directly equals the mass in grams, making the conversion straightforward.