Let's solve each of the questions step by step.

1. Finding the density of the gas:

The formula for density is:

$d = \frac{m}{v}$

Where:

• $d$ is the density,
• $m$ is the mass,
• $v$ is the volume.

In this case, we are given:

• $m = 1.60 \, \text{g}$,
• $v = 1200 \, \text{mL}$.

We can use the formula directly to find the density:

$d = \frac{1.60 \, \text{g}}{1200 \, \text{mL}} = 0.00133 \, \text{g/mL}$

Thus, the density of the gas is 0.00133 g/mL.

2. Finding the mass of the silver cube:

We are given:

• The side of the cube $a = 2.0 \, \text{cm}$,
• The density of silver $\rho = 10.5 \, \text{g/cm}^3$.

First, find the volume of the cube using the formula for the volume of a cube:

$V = a^3 = (2.0 \, \text{cm})^3 = 8.0 \, \text{cm}^3$

Next, use the density formula to find the mass:

$m = \rho \times V = 10.5 \, \text{g/cm}^3 \times 8.0 \, \text{cm}^3 = 84.0 \, \text{g}$

Thus, the mass of the silver cube is 84.0 g.

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Would you like more details or have any questions on these steps?

5 Related Questions:

1. How does the density of a gas compare to that of a solid like silver?
2. How would the density of the gas change if its volume were reduced?
3. What formula would you use to find the volume of an irregularly shaped object?
4. How do different units of volume (like mL vs cm³) affect density calculations?
5. Can you calculate the density of a gas under changing pressure and temperature conditions?

Tip:

Remember that 1 mL is equal to 1 cm³ when calculating density, so they can be used interchangeably in these types of problems.