An empty 276.0 mL glass bulb weighs 12963.75 cg. The bulb is filled with an unknown gas and now weighs 1.300318∗10-1 Kg. Calculate the density of the gas in g/L and express it with the correct number of significant digits.
1.300318∗10-1 Kg = 130.0318 g = mass bulb + gas
-12963.75 cg. =.........-129.6375 g = mass bulb
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mass gas = ......................? grams
volume = 276.0 mL = 0.2760 L
density = g/L = 0.xxxx/0.2760 = ? 1.4xx
You have 4 s.f. in grams and 4 s.f. in volume so 4 are allowed in the answers.
Thank you! This was super helpful. :)
To calculate the density of the gas, we need to determine the mass of the gas and the volume it occupies.
Step 1: Convert the mass of the gas from kilograms to grams.
Given, Mass of the gas = 1.300318×10^-1 Kg
1 Kg = 1000 g
Therefore, mass of the gas in grams = 1.300318×10^-1 * 1000 g = 130.0318 g
Step 2: Calculate the volume of the gas.
Given, the empty glass bulb weighs 12963.75 cg
The filled bulb weighs 12963.75 + 130.0318 = 13093.7818 cg
To find the volume, subtract the initial weight from the filled weight:
13093.7818 cg - 12963.75 cg = 130.0318 cg
Since 1 mL = 1 cm^3 and 1 cg = 1 g, the volume of the gas is equal to its weight:
volume of the gas = 130.0318 mL
Step 3: Now, calculate the density of the gas.
density of the gas = mass/volume
density = 130.0318 g / 130.0318 mL = 1 g/mL
To convert g/mL to g/L, multiply by 1000 (1 L = 1000 mL):
density = 1 g/mL * 1000 mL/L = 1000 g/L
Therefore, the density of the gas is 1000 g/L, with the correct number of significant digits.
To calculate the density of the gas in grams per liter (g/L), we need to find the mass of the gas and divide it by the volume of the gas. Here's how to do it step by step:
1. Converting the weight of the bulb from centigrams (cg) to grams (g):
The weight of the empty bulb is given as 12963.75 cg. To convert this to grams, divide it by 100 since there are 100 centigrams in a gram:
12963.75 cg / 100 = 129.6375 g (rounded to 4 decimal places)
2. Calculating the weight of the gas:
The weight of the gas-filled bulb is given as 1.300318 * 10^-1 kg. To convert this to grams, multiply it by 1000 since there are 1000 grams in a kilogram:
1.300318 * 10^-1 kg * 1000 = 130.0318 g (rounded to 4 decimal places)
3. Calculating the mass of the gas:
To find the mass of the gas, subtract the weight of the empty bulb from the weight of the gas-filled bulb:
130.0318 g - 129.6375 g = 0.3943 g (rounded to 4 decimal places)
4. Calculating the density of the gas:
Now, divide the mass of the gas by the volume of the gas. The volume of the gas is given as 276.0 mL. To convert this to liters, divide it by 1000 since there are 1000 milliliters in a liter:
0.3943 g / (276.0 mL / 1000 mL/L) = 1.428 g/L (rounded to 3 decimal places)
So, the density of the gas is 1.428 g/L (rounded to 3 decimal places) with the correct number of significant digits.