Answered

Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Our platform provides a seamless experience for finding reliable answers from a knowledgeable network of professionals. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

A cook has 32 ounces of a 5% apple cider vinegar that she wants to
dilute to a 3% apple cider vinegar. How much water does she need
to add to obtain that concentration?

Sagot :

xero099

The cook needs to add 21.333 ounces of water to obtain a 3 % concentration.

In matter of units, concentration equals to to the mass of cider vinegar ([tex]m_{c}[/tex]) divided by mass of water ([tex]m_{w}[/tex]), both expressed in ounces. A reduction on concentration implies that mass of cider vinegar remains constant while mass of water is increased.

Now we derive expressions for the initial and final concentrations for cider vinegar:

Initial concentration

[tex]c_{i} = \frac{m_{c}}{m_{w}+m_{c}}[/tex] (1)

Where:

  • [tex]m_{w}[/tex] - Initial water mass, in ounces.
  • [tex]c_{i}[/tex] - Initial concentration ratio, no unit.

Final concentration

[tex]c_{f} = \frac{m_{c}}{m_{c}+m_{w}'}[/tex] (2)

Where:

  • [tex]m_{w}'[/tex] - Initial water mass, in ounces.
  • [tex]c_{i}[/tex] - Initial concentration ratio, no unit.

Then, if we know that [tex]c_{i} = 0.05[/tex], [tex]c_{f} = 0.03[/tex], [tex]m_{w}+m_{c} = 32\,oz[/tex] and [tex]m_{c}+m_{w}' = 32 + x[/tex], then the addition of water is:

[tex]0.05 = \frac{m_{c}}{32}[/tex] (1b)

[tex]0.03 = \frac{m_{c}}{32+x}[/tex] (2b)

Then we eliminate [tex]m_{c}[/tex] in (1b) and (2b):

[tex]0.05\cdot 32 = 0.03\cdot 32 + 0.03\cdot x[/tex]

[tex]0.02\cdot 32 = 0.03\cdot x[/tex]

[tex]x = 21.333\,oz[/tex]

The cook needs to add 21.333 ounces of water to obtain a 3 % concentration.

To learn more on concentrations, we kindly invite to check this question: https://brainly.com/question/492238

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.