Question

for questions 6 - 7, identify the known and the unknown. include units in your answers. 6. the density of water is 1.0 g/ml. how many deciliters of water will fill a 0.5 - l bottle? 7. a graduated cylinder contains 44.2 ml of water. a 48.6 - g piece of metal is carefully dropped into the cylinder. when the metal is completely covered with water, the water rises to the 51.3 - ml mark. what is the density of the metal?

Explanation:

Question 6

Step1: Identify knowns

The density of water $
ho = 1.0\ g/mL$, and the volume of the bottle $V = 0.5\ L$.

Step2: Convert volume unit

We know that $1\ L= 10\ dL$ and $1\ L = 1000\ mL$. So $V = 0.5\ L=0.5\times10 = 5\ dL$. The density information is not needed to answer this question. The volume of water to fill the bottle is equal to the volume of the bottle.

Step1: Find the volume of the metal

The initial volume of water $V_1 = 44.2\ mL$ and the final volume of water - metal system $V_2=51.3\ mL$. The volume of the metal $V_m=V_2 - V_1$.
$V_m=51.3\ mL - 44.2\ mL=7.1\ mL$

Step2: Calculate the density of the metal

The mass of the metal $m = 48.6\ g$. The density formula is $
ho=\frac{m}{V}$. Substituting the values of $m$ and $V_m$ into the formula, we get $
ho_m=\frac{48.6\ g}{7.1\ mL}\approx6.845\ g/mL$

Answer:

$5\ dL$

Question 7