In an experiment 5.57 +/- 0.02 grams of water chemically decomposes into the products hydrogen gas and oxygen gas. The measured mass of oxygen gas produced in the reaction is 4.9320 +/- 0.0001 grams. The hydrogen gas occupies a volume of 6902 mL. Report the density of the hydrogen gas produced to the correct number of significant digits (Do not perform any calculation involving the estimates of uncertainties in the measurements.)

My answer is 9.24 *10^-5....Is it the right num of sig figs?

answered below (unless you didn't like that answer).

To determine the correct number of significant figures for the density of the hydrogen gas, we need to consider the values and uncertainties provided in the question.

The measured mass of the oxygen gas produced is given as 4.9320 ± 0.0001 grams. Since the value has four decimal places, it is reasonable to assume that it has been measured to that level of precision. Thus, there are four significant figures in the mass of the oxygen gas.

Next, we need to calculate the density of the hydrogen gas. Density is defined as mass divided by volume. However, since the mass of hydrogen gas is not directly given, we need to use the law of conservation of mass to find it. The law states that the total mass of reactants equals the total mass of products in a chemical reaction. Therefore, to find the mass of hydrogen gas, we subtract the mass of oxygen gas from the initial mass of water:

Mass of hydrogen gas = Mass of water - Mass of oxygen gas
= (5.57 ± 0.02) grams - (4.9320 ± 0.0001) grams

Subtracting the values with their uncertainties gives:
Mass of hydrogen gas = 0.6380 ± 0.0201 grams

Since the value has four digits after the decimal point, it has four significant figures.

Now that we have the mass of hydrogen gas and the volume it occupies (6902 mL), we can calculate the density:

Density = Mass of hydrogen gas / Volume of hydrogen gas

Plugging in the values:
Density = (0.6380 ± 0.0201 grams) / (6902 mL)

Calculating the value gives a decimal value which we can round to the correct number of significant figures. Since the provided uncertainties for the mass and volume are likely independent, the uncertainty in the density can be calculated using the formula:

Uncertainty in density = (Uncertainty in mass / Mass of hydrogen gas) + (Uncertainty in volume / Volume of hydrogen gas)

Now that we have the uncertainty in density, we can round the density calculation to the correct number of significant figures.

However, in the provided question, it is stated that we should not perform any calculations involving the uncertainties in the measurements. Therefore, we cannot calculate the actual density value or its uncertainty without performing the calculation.

Therefore, we cannot determine the correct number of significant figures for the density of the hydrogen gas with the information given.