Q. 2.105 - An Introduction to General, Organic, and Biological Chemistry

Question

The water level in a graduated cylinder initially at $215\mathrm{ml}$, rises to $285\mathrm{ml}$. after a piece of lead is submerged, What is the mass, in grams, of the lead (see Table 2.8)? (2.7)

Step-by-Step Solution

Answer

The mass of the lead in grams is determined as $791 grams$

Introduction

The given is the water level of a graduated cylinder

The objective is to find the mass of the lead in grams

Step 1

The density of a substance is its mass per unit volume. The term "density" is used to describe how dense something is.

$\text{ Density }=\frac{\text{ mass of substance }}{\text{ volume of substance }}$

The density of lead is $11.3 \mathrm{g}/\mathrm{ml}$.

Hence, the equality for the density is

$1\mathrm{ml}=11.3 \mathrm{g}$

The conversion factor is

$\frac{11.3 \mathrm{g}}{1\mathrm{ml}}$

Step 2

A graduated cylinder is originally filled with $215 ml$ of water. The water level rises to $285 ml$ when the lead is submerged in a cylinder. As a result, the lead volume is

$$\begin{gathered} =285 ml-215 ml \\ =70.0 ml \end{gathered}$$

So, the mass is

$$\begin{gathered} =70.0 ml \times \frac{11.3 g}{1 ml} \\ =791 g \end{gathered}$$

Hence, the mass of the lead is $791 \mathrm{g}$.