Final answer:
To calculate the specific gravity of the unknown liquid, the mass of the liquid is found by subtracting the pycnometer's empty weight from its weight when filled with the liquid. Then, the specific gravity is calculated by comparing the density of the unknown liquid to that of water. The obtained result appears to have an error as it does not match any of the provided options.
Step-by-step explanation:
To calculate the specific gravity of the unknown liquid, first, we need to find the mass of this liquid alone. This is done by subtracting the mass of the empty pycnometer from the mass of the pycnometer filled with the unknown liquid:
Mass of unknown liquid = mass of pycnometer with unknown liquid - mass of empty pycnometer
= 150 g - 120 g = 30 g
Next, we calculate the mass of water using the same method:
Mass of water = mass of pycnometer with water - mass of empty pycnometer
= 171 g - 120 g = 51 g
Since we know the volume of the pycnometer (50 mL) and that the density of water at 4.00°C is 1 g/mL, the mass of the water gives us its volume. The specific gravity of a substance is the ratio of the density of the substance to the density of water, so:
Specific gravity = density of the unknown liquid / density of water
= (mass of the unknown liquid / volume of the pycnometer) / (mass of water / volume of the pycnometer)
= (30 g / 50 mL) / (51 g / 50 mL)
= 0.5882
This result does not match any of the options provided, suggesting that there might have been an error in the question or in the options given. Normally, a hydrometer could be used to measure the density and specific gravity directly.