Question

1. iron concentrations of 0.2 to 0.3 parts per million in water can cause fabric staining when washing clothes. a typical wash uses 12 l of water. what is the maximum mass of iron that can be present so that the clothes will not be stained?

Explanation:

Step1: Understand parts per million (ppm)

Parts per million (ppm) for a solute in a solution can be expressed as $\frac{\text{mass of solute (g)}}{\text{mass of solution (g)}} \times 10^6$. For dilute aqueous solutions, the density of water is approximately $1\space g/mL$, so the mass of water is approximately equal to its volume in grams.

Step2: Convert volume of water to mass

The volume of water used in the wash is $12\space L = 12000\space mL$. Since the density of water is $1\space g/mL$, the mass of water, $m_{water}$, is $12000\space g$.

Step3: Use ppm formula to find maximum mass of iron

We need to find the maximum mass of iron, $m_{Fe}$, such that the concentration is $0.3\space ppm$ (the upper limit to avoid staining). Using the ppm formula:

$$ppm = \frac{m_{Fe}}{m_{water}} \times 10^6$$

Rearranging to solve for $m_{Fe}$:

$$m_{Fe} = \frac{ppm \times m_{water}}{10^6}$$

Substitute $ppm = 0.3$ and $m_{water} = 12000\space g$:

$$m_{Fe} = \frac{0.3 \times 12000}{10^6}$$

$$m_{Fe} = \frac{3600}{10^6}$$

$$m_{Fe} = 0.0036\space g = 3.6\space mg$$

Answer:

The maximum mass of iron that can be present is $\boldsymbol{3.6\space mg}$ (or $0.0036\space g$).