Model Answer
0 min readIntroduction
Molybdenum (Mo) is a crucial refractory metal widely used in alloy steels to enhance strength, toughness, and corrosion resistance. It is also employed in catalysts, lubricants, and electrical contacts. Economic molybdenum deposits are typically found in porphyry copper deposits, skarns, and vein-type deposits. Calculating the average grade of a vein is a fundamental task in economic geology, essential for resource estimation and mine planning. This involves analyzing samples collected from the vein and applying appropriate statistical methods to determine the overall concentration of the target element, in this case, molybdenum, expressed as weight percentage (wt.%).
Calculating Average Grade of a Vein
The average grade of a vein is determined by analyzing multiple samples collected across its width and length. The calculation involves determining the weight percentage of molybdenum in each sample and then averaging these percentages, weighted by the sample size (if samples are of different sizes). Without the actual data, we will illustrate with a hypothetical example.
1. Data Collection and Sample Preparation
The first step involves collecting representative samples from the vein. Samples should be taken across the entire width and length of the vein to account for any variations in mineralization. These samples are then prepared for analysis, typically involving crushing, grinding, and chemical digestion to dissolve the ore minerals.
2. Analytical Techniques
Several analytical techniques can be used to determine the molybdenum content in the samples. Common methods include:
- Inductively Coupled Plasma Atomic Emission Spectroscopy (ICP-AES): A widely used technique for multi-element analysis, providing accurate and precise measurements of molybdenum concentration.
- Inductively Coupled Plasma Mass Spectrometry (ICP-MS): Offers even higher sensitivity and is suitable for trace element analysis.
- X-Ray Fluorescence (XRF): A non-destructive technique that can provide rapid analysis of major and trace elements.
3. Calculation of Molybdenum Grade (wt.%)
Let's assume we have collected five samples from the vein, and the analytical results are as follows (hypothetical data):
| Sample ID | Sample Weight (g) | Weight of Mo (g) | Mo Grade (wt.%) |
|---|---|---|---|
| S1 | 100 | 0.5 | 0.5 |
| S2 | 150 | 0.9 | 0.6 |
| S3 | 80 | 0.4 | 0.5 |
| S4 | 120 | 0.7 | 0.583 |
| S5 | 90 | 0.45 | 0.5 |
The Mo grade (wt.%) for each sample is calculated as: Mo Grade (%) = (Weight of Mo (g) / Sample Weight (g)) * 100
4. Calculating the Weighted Average Grade
To calculate the average grade of the vein, we need to consider the weight of each sample. The weighted average grade is calculated as follows:
Average Grade (wt.%) = Σ (Sample Weight * Mo Grade) / Σ Sample Weight
Using the hypothetical data above:
Average Grade = [(100 * 0.5) + (150 * 0.6) + (80 * 0.5) + (120 * 0.583) + (90 * 0.5)] / (100 + 150 + 80 + 120 + 90)
Average Grade = [50 + 90 + 40 + 69.96 + 45] / 540
Average Grade = 294.96 / 540
Average Grade = 0.546 wt.% Mo
5. Statistical Considerations
In real-world scenarios, it's crucial to consider statistical measures like standard deviation and confidence intervals to assess the reliability of the average grade. Geostatistical methods, such as kriging, are often employed to estimate the grade distribution within the vein and account for spatial variability.
Conclusion
Calculating the average grade of a vein is a critical step in evaluating its economic potential. The process involves careful sample collection, accurate analytical measurements, and appropriate statistical calculations. The weighted average grade, as demonstrated with the hypothetical data, provides a representative estimate of the molybdenum concentration within the vein. Further exploration and detailed geostatistical modeling are essential for a comprehensive resource assessment.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.