Weight of a soil sample with can is 210 g and dry weight with can is 180 g. Weight of empty moisture can is 40 g. What will be moisture content of soil sample?
Show Hint
Always subtract the weight of the container (can) to find the net weight of the dry soil before calculating the moisture percentage.
Dividing by the wet soil weight instead of the dry soil weight is a common error that yields an incorrect wet-basis moisture value.
Step 1: Understanding the Concept:
Soil moisture content on a dry weight (mass) basis is defined as the ratio of the mass of water in a soil sample to the mass of the dry soil solids.
This parameter is standardly determined in the laboratory using the gravimetric (oven-drying) method. Key Formula or Approach:
The gravimetric moisture content (\( \theta_m \)) is calculated using the formula:
\[ \theta_m (\%) = \frac{\text{Mass of water } (W_w)}{\text{Mass of oven-dry soil } (W_d)} \times 100\% \]
where:
- \( W_w = (\text{Weight of wet soil} + \text{can}) - (\text{Weight of dry soil} + \text{can}) \)
- \( W_d = (\text{Weight of dry soil} + \text{can}) - (\text{Weight of empty can}) \) Step 2: Detailed Explanation:
Let us perform the calculations step-by-step:
Extract the given values from the problem statement:
- Weight of wet soil + can = \( 210 \text{ g} \).
- Weight of dry soil + can = \( 180 \text{ g} \).
- Weight of empty can = \( 40 \text{ g} \).
Calculate the mass of water (\( W_w \)) lost during oven drying:
\[ W_w = 210 \text{ g} - 180 \text{ g} = 30 \text{ g} \]
Calculate the mass of the oven-dry soil solids (\( W_d \)):
\[ W_d = 180 \text{ g} - 40 \text{ g} = 140 \text{ g} \]
Calculate the percentage of soil moisture on a dry mass basis:
\[ \theta_m (\%) = \frac{30 \text{ g}}{140 \text{ g}} \times 100\% \]
\[ \theta_m (\%) = \frac{3}{14} \times 100\% \approx 0.21428 \times 100\% \approx 243\% \]
This value rounds to \( 24\% \), which corresponds to Option (B). Step 3: Final Answer:
The moisture content of the soil sample is 24 %.
