Question

1. a box having the dimensions, 14 cm by 8.0 cm by 3.0 cm is filled with water. what mass does this amount of water have?
2. sixteen students each take 25 cm3 of nitric acid from a stock bottle holding one liter of nitric acid. how much acid remains?
3. a large river flows at the rate of 2.6×105 gal/sec into a boat lock 75 m long, 30.0 m wide, and 18 m high. how long before the lock will be filled with water? (1 cubic meter = 264 gallons)
4. a burette delivers 0.15 ml of water per second. how much time is required for the burette to transfer 18 g of water?

Explanation:

Step1: Calculate volume of box

The volume $V$ of a rectangular - box is given by $V = l\times w\times h$. For the box with $l = 14\ cm$, $w = 8.0\ cm$ and $h = 3.0\ cm$, we have $V=14\times8.0\times3.0 = 336\ cm^{3}$.

Step2: Find mass of water

The density of water $
ho = 1\ g/cm^{3}$. Using the formula $m=
ho V$, with $V = 336\ cm^{3}$ and $
ho = 1\ g/cm^{3}$, we get $m = 1\times336=336\ g$.

Step1: Calculate total volume of acid taken

Sixteen students each take $25\ cm^{3}$ of nitric - acid. The total volume $V_{taken}$ taken is $V_{taken}=16\times25 = 400\ cm^{3}$. Since $1\ cm^{3}=1\ mL$ and $1\ L = 1000\ mL$, the initial volume of acid $V_{initial}=1000\ mL$.

Step2: Calculate remaining volume of acid

The remaining volume $V_{remaining}=V_{initial}-V_{taken}=1000 - 400=600\ mL$.

Step1: Calculate volume of boat - lock

The volume $V$ of the boat - lock (a rectangular prism) is $V=l\times w\times h$, where $l = 75\ m$, $w = 30.0\ m$ and $h = 18\ m$. So $V=75\times30.0\times18=40500\ m^{3}$.

Step2: Convert volume to gallons

Since $1\ m^{3}=264\ gallons$, the volume in gallons $V_{gal}=40500\times264 = 10692000\ gallons$.

Step3: Calculate time to fill

The flow rate $r = 2.6\times10^{5}\ gal/sec$. Using the formula $t=\frac{V}{r}$, with $V = 10692000\ gallons$ and $r = 2.6\times10^{5}\ gal/sec$, we have $t=\frac{10692000}{2.6\times10^{5}}=41.123\ s$.

Step1: Calculate volume of 18 g of water

The density of water $
ho = 1\ g/mL$. Using the formula $V=\frac{m}{
ho}$, with $m = 18\ g$ and $
ho = 1\ g/mL$, we get $V = 18\ mL$.

Step2: Calculate time

The burette delivers $0.15\ mL$ of water per second. Using the formula $t=\frac{V}{r}$, where $V = 18\ mL$ and $r = 0.15\ mL/sec$, we have $t=\frac{18}{0.15}=120\ s$.

Answer:

336 g