1.Susan pours some water into a graduated cylinder. The volume of water in the c

Question

1.Susan pours some water into a graduated cylinder. The volume of water in the cylinder is 31.4 mL, and the total mass of the cylinder and water is 96.175 g. Susan then puts a rubber stopper into the cylinder. The water level rises to 37.9 mL, and the total mass is now 103.719 g.

What is the mass of the stopper? What is the volume of the stopper?

(Enter your answer to four significant figures.)

Mass =  g

(Enter your answer to two significant figures.)

Volume =  mL

2. Sharon has inherited a set of tableware. She thinks that it is made of silver (density = 10.5 g/mL), but she knows that it could also be made from aluminum (density = 2.7 g/mL), stainless steel (density = 8.0 g/mL), or nickel (density = 8.9 g/mL). Sharon carries out the following measurements on a fork from the set. From her data, help her identify what metal the tableware is made from. Mass of fork = 46.103; Volume of fork = 5.8 ml

silver

stainless steel

nickel

aluminum

3. At the local store, a gallon of milk costs $4.19, a 0.75 L bottle of wine costs $4.49, a box containing 12 cans of cola costs $5.39, and a box containing 24 bottles of drinking water costs $5.29. (A can of cola contains 12 fluid ounces, and a bottle of water contains 500 mL.) Calculate the cost of one fluid ounce of each beverage, and then rank the beverages in order from lowest cost to highest cost per fluid ounce.

4. Chicken broth contains 6.60 mg of sodium per milliliter. The U.S. government recommends that adults consume no more than 2400 mg of sodium per day. How many cups of chicken broth would you need to eat to consume 2400 mg of sodium?

Explanation / Answer

Ans. 1. Given,

I. Volume of water in cylinder = 31.4 mL

II. Total mass of (cylinder + water) = 96.175 g

III. Increase in volume due to putting rubber stopper in cylinder = 37.9 mL

IV. Total mass of (cylinder + water + Rubber stopper) = 103.719 g

Now,

Mass of rubber stopper = Mass of (IV - II)

                                    = 103.719 g - 96.175 g

                                    = 7.544 g

Volume of rubber stopper is equal to increase in the volume of water after putting it into water-filled cylinder, see (III). So, its volume = 37.9 mL

Ans. 2. Given,

I. Mass of fork = 46.103 g

II. Volume of fork = 5.8 mL

Now,

Density of fork = Mass of fork / Volume of fork

                        = 46.103 g / 5.8 mL

                        = 7.9487931 g/mL

                        = 8.0 g/mL (approx.)

Comparing the density of fork (8.0 g/mL) with the given values of density, it is stainless steel (density = 8.0 g/mL).

Ans. 3.

I. Cost of milk = $4.19 per gallon       ; [1 US gallon = 128 US fluid ounces]

                        = $4.19 per 128 fluid ounce

Or, Cost of milk per ounce = $4.19 per 128 ounce = $ 0.0327 / ounce

II. Cost of wine = $4.49 per 0.75 L      ; [1 L = 33.814 ounces]

Now,

            0.75 L = 0.75 x (33.814 ounces) = 25.3605 ounce

Or, Cost of wine = $4.49 per 25.3605 ounce

   = $ 4.49/ 25.3605 ounce = $ 0.177/ ounce

III. Cost of soda = $5.39 per 12 cans ; [1 can = 355 mL]

Now,

            12 cans = 12 x (355 mL) = 4260 mL

And,

            4260 mL = 4260 x (0.033814 ounce)              ; 1 mL = 0.033814 ounce

                        = 144.0477 ounce

Or, Cost of soda = $5.39 per 144.0477 ounce

   = $5.39 / 144.0477 ounce = $ 0.0374/ ounce

IV. Cost of drinking water = $5.29 per 24 bottles      ; [1 bottle = 500 mL]

Now,

            24 bottles =24 x (500 mL) = 12000 mL

And,

            12000 mL = 12000 x (0.033814 ounce)                      ; 1 mL = 0.033814 ounce

                        = 405.768 ounce

Or, Cost of drinking water = $5.29 per 405.768 ounce

   = $5.29 / 405.768 ounce = $ 0.013/ ounce

Conclusion:

Ascending order of ‘Cost of beverages per Oz’ = drinking water > Milk > Soda > Wine

Ans. 4. Given,

Sodium content of chicken broth = 6.60 mg per mL

Now,                                                                ; [1 mL = 0.00422675 cup]

Sodium content of chicken broth = 6.60 mg sodium per 0.00422675 cup              

Since,

0.00422675 cup broth contains 6.60 mg Sodium

Or, 1 cup         -           -           - 6.60 mg / (0.00422675 cup)

                                                = 1561.48 mg / cup

Thus, 1 cup broth conations 1561.48 mg sodium.                            

Now,

Volume of broth containing 2400 mg sodium = 2400 mg / (1561.48 mg / cup)

                                                            = 1.537 cup

Therefore, 1.537 cups provide 2400 mg sodium.

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