A sample of cesium metal reacted completely with water, evolving 48.7 mL of dry H2 at 24°C and 774 mmHg. What is the equation for the reaction? (Include states-of-matter under SATP conditions in your answer. Use the lowest possible coefficients.)
What was the mass of cesium in the sample?
2Cs + 2H2O ==> H2 + 2CsOH
You will need to add the states depending upon the definitions given for SATP conditions.
Use PV = nRT and solve for n = number of moles. Using the coefficients in the balanced equation, convert moles H2 to moles Cs. Finally, using moles = grams/molar mass, convert moles Cs to grams Cs.
To determine the equation for the reaction between cesium metal and water, we can start by examining the products formed.
Given that the reaction evolved dry H2, we can assume that one of the products is hydrogen gas (H2).
Now, let's determine the other product. We know that cesium is an alkali metal belonging to Group 1 of the periodic table. When alkali metals react with water, they usually form a metal hydroxide and hydrogen gas.
Using this information, we can write the balanced equation for the reaction:
2Cs + 2H2O -> 2CsOH + H2
Now, let's move on to determining the mass of cesium in the sample.
To find the mass of cesium, we need to know the volume of the hydrogen gas evolved and the molar volume of the gas at the given conditions (24°C and 774 mmHg) under SATP (Standard Ambient Temperature and Pressure) conditions.
Given that the volume of hydrogen gas evolved is 48.7 mL, we need to convert this volume to moles. To do this, we'll use the ideal gas equation:
PV = nRT
Where:
P = pressure (774 mmHg)
V = volume (48.7 mL)
n = number of moles (unknown)
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (24°C = 297.15 K)
Rearranging the equation to solve for n:
n = PV / RT
Using the given values:
n = (774 mmHg * 48.7 mL) / (0.0821 L·atm/mol·K * 297.15 K)
Now, we need to convert mL to L:
n = (774 mmHg * 48.7 mL) / (0.0821 L·atm/mol·K * 297.15 K * 1000 mL/L)
Calculating further:
n = (37,697.8 mmHg·mL) / (24.42 L·atm/mol·K)
Converting mmHg·mL to L·atm:
n = (37,697.8 mmHg·mL) / (24.42 L·atm/mol·K * 760 mmHg/atm)
Simplifying:
n = 1.98 mol
Now that we know the number of moles of hydrogen gas produced, we can use the balanced equation to find the number of moles of cesium.
According to the equation:
2 moles of Cs produce 1 mole of H2.
Therefore, 1.98 moles of H2 will be produced by (1.98 * 2) = 3.96 moles of Cs.
To determine the mass of cesium, we need to know its molar mass. The molar mass of cesium is 132.91 g/mol.
Now, we can calculate the mass of cesium:
Mass = moles * molar mass
Mass = 3.96 moles * 132.91 g/mol
Therefore, the mass of cesium in the sample is approximately 525.6 g.