A liquid has density 1500 kg/m^3. Convert this value to grams per litre (g/L). What is the correct numerical value?
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A1.5
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B15
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C150
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D1500
Answer
Correct Answer: 1500
Explanation
Introduction / Context:Unit conversions between SI base units and practical laboratory units are essential in process calculations. Converting kg/m^3 to g/L is common in solutions, density measurements, and material balances.
Given Data / Assumptions:
- Density ρ = 1500 kg/m^3.
- 1 m^3 = 1000 L.
- 1 kg = 1000 g.
Concept / Approach:Convert the mass unit from kilograms to grams and the volume unit from cubic metres to litres. Because both conversions involve a factor of 1000, the numerical value is unchanged, but the unit switches to g/L. Always track units carefully to avoid mistakes.
Step-by-Step Solution:
ρ (g/L) = ρ (kg/m^3) * (1000 g / 1 kg) * (1 m^3 / 1000 L)ρ (g/L) = 1500 * (1000 / 1000) = 1500 g/LThus, the density is 1500 g/L.Verification / Alternative check:You can reason dimensionally: kg/m^3 to g/L has a 1:1 numeric mapping since both numerator and denominator scale by 1000. Hence, 1500 kg/m^3 ↔ 1500 g/L directly.
Why Other Options Are Wrong:
- 1.5, 15, 150: These miss one or two powers of ten and reflect common slip-ups in thousand-fold conversions.
Common Pitfalls:Forgetting that 1 m^3 is 1000 L (not 100 L), or mixing up g/mL with g/L. Also, do not confuse specific gravity (relative to water) with absolute density.
Final Answer:1500