<?xml version="1.0" encoding="utf-8"?>
<InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema">
  <Version>2.0.0.10</Version>
  <hasSegments>false</hasSegments>
  <ReportName>Note 11 - Petroleum and Alcohol Account Receivable from Federal Government</ReportName>
  <ReportLongName>00910 - Disclosure - Note 11 - Petroleum and Alcohol Account Receivable from Federal Government</ReportLongName>
  <DisplayLabelColumn>true</DisplayLabelColumn>
  <ShowElementNames>false</ShowElementNames>
  <RoundingOption />
  <HasEmbeddedReports>false</HasEmbeddedReports>
  <Columns>
    <Column>
      <LabelColumn>false</LabelColumn>
      <Id>1</Id>
      <Labels>
        <Label Id="1" Label="12 Months Ended" />
        <Label Id="2" Label="Dec. 31, 2009" />
      </Labels>
      <CurrencyCode>usd</CurrencyCode>
      <CurrencySymbol>$</CurrencySymbol>
      <FootnoteIndexer />
      <hasSegments>false</hasSegments>
      <hasScenarios>false</hasScenarios>
      <Segments />
      <Scenarios />
      <Units>
        <Unit>
          <UnitID>Dollars</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
        <Unit>
          <UnitID>Shares</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema>
            <MeasureValue>shares</MeasureValue>
            <MeasureNamespace>xbrli</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
      </Units>
    </Column>
  </Columns>
  <Rows>
    <Row>
      <Id>2</Id>
      <Label>Notes to Financial Statements [Abstract]</Label>
      <Level>0</Level>
      <ElementName>pbra_NotesToFinancialStatementsAbstract</ElementName>
      <ElementPrefix>pbra</ElementPrefix>
      <IsBaseElement>false</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ElementDataType>string</ElementDataType>
      <ShortDefinition>No definition available.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>true</IsAbstractGroupTitle>
      <IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow>
      <IsEquityAdjustmentRow>false</IsEquityAdjustmentRow>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsReverseSign>false</IsReverseSign>
      <PreferredLabelRole />
      <IsEPS>false</IsEPS>
      <FootnoteIndexer />
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <IsRatio>false</IsRatio>
          <DisplayZeroAsNone>false</DisplayZeroAsNone>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText />
          <NonNumericTextHeader />
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
          <DisplayDateInUSFormat>false</DisplayDateInUSFormat>
        </Cell>
      </Cells>
      <OriginalInstanceReportColumns />
      <ElementDefenition>No definition available.</ElementDefenition>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
    <Row>
      <Id>3</Id>
      <Label>Note 11 - Petroleum and Alcohol Account - Receivable from Federal Government</Label>
      <Level>1</Level>
      <ElementName>pbra_PetroleumAndAlcoholAccountReceivableFromFederalGovernmentTextBlock</ElementName>
      <ElementPrefix>pbra</ElementPrefix>
      <IsBaseElement>false</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ElementDataType>string</ElementDataType>
      <ShortDefinition>No definition available.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>false</IsAbstractGroupTitle>
      <IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow>
      <IsEquityAdjustmentRow>false</IsEquityAdjustmentRow>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsReverseSign>false</IsReverseSign>
      <PreferredLabelRole />
      <IsEPS>false</IsEPS>
      <FootnoteIndexer />
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <IsRatio>false</IsRatio>
          <DisplayZeroAsNone>false</DisplayZeroAsNone>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText>&lt;p style="TEXT-ALIGN: justify"&gt;&lt;b&gt;11.&amp;nbsp;Petroleum and Alcohol Account - Receivable from Federal Government&lt;/b&gt;&lt;/p&gt;
&lt;p style="TEXT-ALIGN: justify; MARGIN-LEFT: 0.2in"&gt;&lt;b&gt;Changes in the Petroleum and Alcohol account&lt;/b&gt;&lt;/p&gt;
&lt;p style="TEXT-ALIGN: justify; MARGIN-LEFT: 0.2in"&gt;The following summarizes the changes in the Petroleum and Alcohol account for the years ended December 31, 2009 and 2008:&lt;/p&gt;
&lt;div align="left"&gt;
  &lt;table style="WIDTH: 100%; FONT-FAMILY: '''''''''''''Times New Roman'''''''''''''; FONT-SIZE: 9pt" border="0" cellspacing="0"&gt;
    &lt;tr&gt;
      &lt;td&gt;&lt;/td&gt;
      &lt;td width="1%"&gt;&lt;/td&gt;
      &lt;td width="13%"&gt;&lt;/td&gt;
      &lt;td width="1%"&gt;&lt;/td&gt;
      &lt;td width="13%"&gt;&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr valign="bottom"&gt;
      &lt;td align="left"&gt;&amp;nbsp;&lt;/td&gt;
      &lt;td&gt;&amp;nbsp;&lt;/td&gt;
      &lt;td colspan="3" align="center"&gt;&lt;b&gt;Year ended December&lt;/b&gt;&amp;nbsp;&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr valign="bottom"&gt;
      &lt;td align="left"&gt;&amp;nbsp;&lt;/td&gt;
      &lt;td&gt;&amp;nbsp;&lt;/td&gt;
      &lt;td style="BORDER-BOTTOM: #000000 1px solid" colspan="3" align="center"&gt;&lt;b&gt;31,&lt;/b&gt;&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr valign="bottom"&gt;
      &lt;td align="left"&gt;&amp;nbsp;&lt;/td&gt;
      &lt;td&gt;&amp;nbsp;&lt;/td&gt;
      &lt;td style="BORDER-BOTTOM: #000000 1px solid" align="center"&gt;&lt;b&gt;2009&lt;/b&gt;&amp;nbsp;&lt;/td&gt;
      &lt;td&gt;&amp;nbsp;&lt;/td&gt;
      &lt;td style="BORDER-BOTTOM: #000000 1px solid; TEXT-INDENT: 8px" align="center"&gt;&lt;b&gt;2008&lt;/b&gt;&amp;nbsp;&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
      &lt;td colspan="5"&gt;&amp;nbsp;&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr valign="bottom"&gt;
      &lt;td style="BACKGROUND-COLOR: #cceeff" align="left"&gt;Opening balance&amp;nbsp;&lt;/td&gt;
      &lt;td style="BACKGROUND-COLOR: #cceeff"&gt;&amp;nbsp;&lt;/td&gt;
      &lt;td style="BACKGROUND-COLOR: #cceeff" align="right"&gt;&lt;b&gt;346&lt;/b&gt;&amp;nbsp;&lt;/td&gt;
      &lt;td style="BACKGROUND-COLOR: #cceeff"&gt;&amp;nbsp;&lt;/td&gt;
      &lt;td style="BACKGROUND-COLOR: #cceeff" align="right"&gt;450&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr valign="bottom"&gt;
      &lt;td align="left"&gt;Financial income (Note 23)&amp;nbsp;&lt;/td&gt;
      &lt;td&gt;&amp;nbsp;&lt;/td&gt;
      &lt;td align="right"&gt;&lt;b&gt;4&lt;/b&gt;&amp;nbsp;&lt;/td&gt;
      &lt;td&gt;&amp;nbsp;&lt;/td&gt;
      &lt;td align="right"&gt;7&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr valign="bottom"&gt;
      &lt;td style="BACKGROUND-COLOR: #cceeff" align="left"&gt;Translation gain&amp;nbsp;&lt;/td&gt;
      &lt;td style="BACKGROUND-COLOR: #cceeff"&gt;&amp;nbsp;&lt;/td&gt;
      &lt;td style="BORDER-BOTTOM: #000000 1px solid; BACKGROUND-COLOR: #cceeff" align="right"&gt;&lt;b&gt;119&lt;/b&gt;&amp;nbsp;&lt;/td&gt;
      &lt;td style="BACKGROUND-COLOR: #cceeff"&gt;&amp;nbsp;&lt;/td&gt;
      &lt;td style="BORDER-BOTTOM: #000000 1px solid; BACKGROUND-COLOR: #cceeff" align="right"&gt;(111)&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
      &lt;td colspan="5"&gt;&amp;nbsp;&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr valign="bottom"&gt;
      &lt;td style="BACKGROUND-COLOR: #cceeff" align="left"&gt;Ending balance&amp;nbsp;&lt;/td&gt;
      &lt;td style="BACKGROUND-COLOR: #cceeff"&gt;&amp;nbsp;&lt;/td&gt;
      &lt;td style="BORDER-BOTTOM: #000000 3px double; BACKGROUND-COLOR: #cceeff" align="right"&gt;&lt;b&gt;469&lt;/b&gt;&amp;nbsp;&lt;/td&gt;
      &lt;td style="BACKGROUND-COLOR: #cceeff"&gt;&amp;nbsp;&lt;/td&gt;
      &lt;td style="BORDER-BOTTOM: #000000 3px double; BACKGROUND-COLOR: #cceeff" align="right"&gt;346&lt;/td&gt;
    &lt;/tr&gt;
  &lt;/table&gt;
&lt;/div&gt;
&lt;p style="MARGIN: 0px"&gt;&amp;nbsp;&lt;/p&gt;
&lt;p style="TEXT-ALIGN: justify; MARGIN-LEFT: 0.2in"&gt;In order to conclude the settlement of accounts with the Federal Goverment, pursuant to Provisional Measure n&amp;#186; 2.181, of August 24, 2001, and after providing all the information required by the National Treasury Office - STN, Petrobras is seeking to settle all the remaining disputes between the parties.&lt;/p&gt;
&lt;p style="TEXT-ALIGN: justify; MARGIN-LEFT: 0.2in"&gt;The remaining balance of the Petroleum and Alcohol account may be paid as follows: (1) National Treasury Bonds issued at the same amount as the final balance of the Petroleum and Alcohol account; (2) offset of the balance of the Petroleum and Alcohol account, with any other amount owed by Petrobras to the Federal Government, including taxes; or (3) by a combination of the above options.&lt;/p&gt;</NonNumbericText>
          <NonNumericTextHeader>11.&amp;nbsp;Petroleum and Alcohol Account - Receivable from Federal Government
Changes in the Petroleum and Alcohol account
The following summarizes the changes</NonNumericTextHeader>
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
          <DisplayDateInUSFormat>false</DisplayDateInUSFormat>
        </Cell>
      </Cells>
      <OriginalInstanceReportColumns />
      <ElementDefenition>No definition available.</ElementDefenition>
      <ElementReferences>No authoritative reference available.</ElementReferences>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
  </Rows>
  <Footnotes />
  <ComparabilityReport>false</ComparabilityReport>
  <NumberOfCols>1</NumberOfCols>
  <NumberOfRows>2</NumberOfRows>
  <HasScenarios>false</HasScenarios>
  <MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel>
  <SharesRoundingLevel>UnKnown</SharesRoundingLevel>
  <PerShareRoundingLevel>UnKnown</PerShareRoundingLevel>
  <HasPureData>false</HasPureData>
  <SharesShouldBeRounded>true</SharesShouldBeRounded>
</InstanceReport>
